Effectively calculable quantum mechanics
Bolotin, Arkady
2015-01-01
According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are associated with Fibonacci numbers, this paper shows that the mathematical formalism of quantum mechanics is non-constructive since it permits an undecidable (or effectively impossible) subset of Hilbert space. On the other hand, as it is argued in the paper, if...
Challenges in Large Scale Quantum Mechanical Calculations
Ratcliff, Laura E; Huhs, Georg; Deutsch, Thierry; Masella, Michel; Genovese, Luigi
2016-01-01
During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles calculations of systems containing up to a few hundred atoms have become a standard in many branches of science. The sizes of the systems which can be simulated have increased even further during recent years, and quantum-mechanical calculations of systems up to many thousands of atoms are nowadays possible. This opens up new appealing possibilities, in particular for interdisciplinary work, bridging together communities of different needs and sensibilities. In this review we will present the current status of this topic, and will also give an outlook on the vast multitude of applications, challenges and opportunities stimulated by electronic structure calculations, making this field an important working tool and bringing together researchers of many different domains.
Quantum mechanical calculations and mineral spectroscopy
Kubicki, J. D.
2006-05-01
Interpretation of spectra in systems of environmental interest is not generally straightforward due to the lack of close analogs and a clear structure of some components of the system. Computational chemistry can be used as an objective method to test interpretations of spectra. This talk will focus on applying ab initio methods to complement vibrational, NMR, and EXAFS spectroscopic information. Examples of systems studied include phosphate/Fe-hydroxides, arsenate/Al- and Fe-hydroxide, fractured silica surfaces. Phosphate interactions with Fe-hydroxides are important in controlling nutrient availability in soils and transport within streams. In addition, organo-phosphate bonding may be a key attachment mechanism for bacteria at Fe-oxide surfaces. Interpretation of IR spectra is enhanced by model predictions of vibrational frequencies for various surface complexes. Ab initio calculations were used to help explain As(V) and As(III) adsorption behavior onto amorphous Al- and Fe-hydroxides in conjunction with EXAFS measurements. Fractured silica surfaces have been implicated in silicosis. These calculations test structures that could give rise to radical formation on silica surfaces. Calculations to simulate the creation of Si and SiO radical species on sufaces and their subsequent production of OH radicals will be discussed.
Monte-carlo calculations for some problems of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Novoselov, A. A., E-mail: novoselov@goa.bog.msu.ru; Pavlovsky, O. V.; Ulybyshev, M. V. [Moscow State University (Russian Federation)
2012-09-15
The Monte-Carlo technique for the calculations of functional integral in two one-dimensional quantum-mechanical problems had been applied. The energies of the bound states in some potential wells were obtained using this method. Also some peculiarities in the calculation of the kinetic energy in the ground state had been studied.
Importance of parametrizing constraints in quantum-mechanical variational calculations
Chung, Kwong T.; Bhatia, A. K.
1992-01-01
In variational calculations of quantum mechanics, constraints are sometimes imposed explicitly on the wave function. These constraints, which are deduced by physical arguments, are often not uniquely defined. In this work, the advantage of parametrizing constraints and letting the variational principle determine the best possible constraint for the problem is pointed out. Examples are carried out to show the surprising effectiveness of the variational method if constraints are parameterized. It is also shown that misleading results may be obtained if a constraint is not parameterized.
Quantum-Mechanical Calculations on Molecular Substructures Involved in Nanosystems
Directory of Open Access Journals (Sweden)
Beata Szefler
2014-09-01
Full Text Available In this review article, four ideas are discussed: (a aromaticity of fullerenes patched with flowers of 6-and 8-membered rings, optimized at the HF and DFT levels of theory, in terms of HOMA and NICS criteria; (b polybenzene networks, from construction to energetic and vibrational spectra computations; (c quantum-mechanical calculations on the repeat units of various P-type crystal networks and (d construction and stability evaluation, at DFTB level of theory, of some exotic allotropes of diamond D5, involved in hyper-graphenes. The overall conclusion was that several of the yet hypothetical molecular nanostructures herein described are serious candidates to the status of real molecules.
Conformational analysis of small molecules: NMR and quantum mechanics calculations.
Tormena, Cláudio F
2016-08-01
This review deals with conformational analysis in small organic molecules, and describes the stereoelectronic interactions responsible for conformational stability. Conformational analysis is usually performed using NMR spectroscopy through measurement of coupling constants at room or low temperature in different solvents to determine the populations of conformers in solution. Quantum mechanical calculations are used to address the interactions responsible for conformer stability. The conformational analysis of a large number of small molecules is described, using coupling constant measurements in different solvents and at low temperature, as well as recent applications of through-space and through-hydrogen bond coupling constants JFH as tools for the conformational analysis of fluorinated molecules. Besides NMR parameters, stereoelectronic interactions such as conjugative, hyperconjugative, steric and intramolecular hydrogen bond interactions involved in conformational preferences are discussed.
A perspective on quantum mechanics calculations in ADMET predictions.
Bowen, J Phillip; Güner, Osman F
2013-01-01
Understanding the molecular basis of drug action has been an important objective for pharmaceutical scientists. With the increasing speed of computers and the implementation of quantum chemistry methodologies, pharmacodynamic and pharmacokinetic problems have become more computationally tractable. Historically the former has been the focus of drug design, but within the last two decades efforts to understand the latter have increased. It takes about fifteen years and over $1 billion dollars for a drug to go from laboratory hit, through lead optimization, to final approval by the U.S. Food and Drug Administration. While the costs have increased substantially, the overall clinical success rate for a compound to emerge from clinical trials is approximately 10%. Most of the attrition rate can be traced to ADMET (absorption, distribution, metabolism, excretion, and toxicity) problems, which is a powerful impetus to study these issues at an earlier stage in drug discovery. Quantum mechanics offers pharmaceutical scientists the opportunity to investigate pharmacokinetic problems at the molecular level prior to laboratory preparation and testing. This review will provide a perspective on the use of quantum mechanics or a combination of quantum mechanics coupled with other classical methods in the pharmacokinetic phase of drug discovery. A brief overview of the essential features of theory will be discussed, and a few carefully selected examples will be given to highlight the computational methods.
The Calculation of Matrix Elements in Relativistic Quantum Mechanics
Ilarraza-Lomelí, A. C.; Valdés-Martínez, M. N.; Salas-Brito, A. L.; Martínez-y-Romero, R. P.; Núñez-Yépez, H. N
2001-01-01
Employing a relativistic version of a hypervirial result, recurrence relations for arbitrary non-diagonal radial hydrogenic matrix elements have recently been obtained in Dirac relativistic quantum mechanics. In this contribution honoring Professor L\\"owdin, we report on a new relation we have recently discovered between the matrix elements $$ and $$---where $\\beta$ is a Dirac matrix and the numbers distiguish between different radial eigenstates--- that allow for a simplification and hence f...
PDB ligand conformational energies calculated quantum-mechanically.
Sitzmann, Markus; Weidlich, Iwona E; Filippov, Igor V; Liao, Chenzhong; Peach, Megan L; Ihlenfeldt, Wolf-Dietrich; Karki, Rajeshri G; Borodina, Yulia V; Cachau, Raul E; Nicklaus, Marc C
2012-03-26
(RSCC). We repeated these calculations with the solvent model IEFPCM, which yielded energy differences that were generally somewhat lower than the corresponding vacuum results but did not produce a qualitatively different picture. Torsional sampling around the crystal conformation at the molecular mechanics level using the MMFF94s force field typically led to an increase in energy. © 2012 American Chemical Society
Jia, Xiangyu; Wang, Meiting; Shao, Yihan; König, Gerhard; Brooks, Bernard R; Zhang, John Z H; Mei, Ye
2016-02-09
In this work, the solvation free energies of 20 organic molecules from the 4th Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL4) have been calculated. The sampling of phase space is carried out at a molecular mechanical level, and the associated free energy changes are estimated using the Bennett Acceptance Ratio (BAR). Then the quantum mechanical (QM) corrections are computed through the indirect Non-Boltzmann Bennett's acceptance ratio (NBB) or the thermodynamics perturbation (TP) method. We show that BAR+TP gives a minimum analytic variance for the calculated solvation free energy at the Gaussian limit and performs slightly better than NBB in practice. Furthermore, the expense of the QM calculations in TP is only half of that in NBB. We also show that defining the biasing potential as the difference of the solute-solvent interaction energy, instead of the total energy, can converge the calculated solvation free energies much faster but possibly to different values. Based on the experimental solvation free energies which have been published before, it is discovered in this study that BLYP yields better results than MP2 and some other later functionals such as B3LYP, M06-2X, and ωB97X-D.
Young’s modulus calculations for cellulose Iß by MM3 and quantum mechanics
Quantum mechanics (QM) and molecular mechanics (MM) calculations were performed to elucidate Young’s moduli for a series of cellulose Iß models. Computations using the second generation empirical force field MM3 with a disaccharide cellulose model, 1,4'-O-dimethyl-ß-cellobioside (DMCB), and an analo...
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Steinmann, Casper; Olsen, Jógvan Magnus Haugaard; Kongsted, Jacob
2014-01-01
We present NMR shielding constants obtained through quantum mechanical/molecular mechanical (QM/MM) embedding calculations. Contrary to previous reports, we show that a relatively small QM region is sufficient, provided that a high-quality embedding potential is used. The calculated averaged NMR...
Moreira, Cátia; Ramos, Maria J; Fernandes, Pedro Alexandrino
2016-06-27
This paper is devoted to the understanding of the reaction mechanism of mycobacterium tuberculosis glutamine synthetase (mtGS) with atomic detail, using computational quantum mechanics/molecular mechanics (QM/MM) methods at the ONIOM M06-D3/6-311++G(2d,2p):ff99SB//B3LYP/6-31G(d):ff99SB level of theory. The complete reaction undergoes a three-step mechanism: the spontaneous transfer of phosphate from ATP to glutamate upon ammonium binding (ammonium quickly loses a proton to Asp54), the attack of ammonia on phosphorylated glutamate (yielding protonated glutamine), and the deprotonation of glutamine by the leaving phosphate. This exothermic reaction has an activation free energy of 21.5 kcal mol(-1) , which is consistent with that described for Escherichia coli glutamine synthetase (15-17 kcal mol(-1) ). The participating active site residues have been identified and their role and energy contributions clarified. This study provides an insightful atomic description of the biosynthetic reaction that takes place in this enzyme, opening doors for more accurate studies for developing new anti-tuberculosis therapies.
Biswas, P K; Gogonea, V
2005-10-22
We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical (QM)-molecular-mechanical (MM) calculations. To remedy the nonphysical QM/MM Coulomb interaction at short distances arising from a point electrostatic potential (ESP) charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge and describe the effect of a s-wave expansion, extended over the covalent radius r(c), of the MM atom. The resulting potential describes that, at short distances, large scale cancellation of Coulomb interaction arises intrinsically from the localized expansion of the MM point charge and the potential self-consistently reduces to 1r(c) at zero distance providing a renormalization to the Coulomb energy near interatomic separations. Employing this renormalized Hamiltonian, we developed an interface between the Car-Parrinello molecular-dynamics program and the classical molecular-dynamics simulation program Groningen machine for chemical simulations. With this hybrid code we performed QM/MM calculations on water dimer, imidazole carbon monoxide (CO) complex, and imidazole-heme-CO complex with CO interacting with another imidazole. The QM/MM results are in excellent agreement with experimental data for the geometry of these complexes and other computational data found in literature.
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Isabella Natali Sora
2012-01-01
Full Text Available Quantum mechanics density functional calculations provided gas-phase electron distributions and proton affinities for several mono- and diaza[5]helicenes; computational results, together with experimental data concerning crystal structures and propensity to methylation of the nitrogen atom(s, provide a basis for designing azahelicene complexes with transition metal ions.
Kamachi, Takashi; Yoshizawa, Kazunari
2016-02-22
A conformational search program for finding low-energy conformations of large noncovalent complexes has been developed. A quantitatively reliable semiempirical quantum mechanical PM6-DH+ method, which is able to accurately describe noncovalent interactions at a low computational cost, was employed in contrast to conventional conformational search programs in which molecular mechanical methods are usually adopted. Our approach is based on the low-mode method whereby an initial structure is perturbed along one of its low-mode eigenvectors to generate new conformations. This method was applied to determine the most stable conformation of transition state for enantioselective alkylation by the Maruoka and cinchona alkaloid catalysts and Hantzsch ester hydrogenation of imines by chiral phosphoric acid. Besides successfully reproducing the previously reported most stable DFT conformations, the conformational search with the semiempirical quantum mechanical calculations newly discovered a more stable conformation at a low computational cost.
Zhang, Dawei
2017-03-01
Molecular fractionation with conjugate caps (MFCC) method is introduced for the efficient estimation of quantum mechanical (QM) interaction energies between nanomaterial (carbon nanotube, fullerene, and graphene surface) and ligand (charged and neutral). In the calculations, nanomaterials are partitioned into small fragments and conjugated caps that are properly capped, and the interaction energies can be obtained through the summation of QM calculations of the fragments from which the contribution of the conjugated caps is removed. All the calculations were performed by density functional theory (DFT) and dispersion contributions for the attractive interactions were investigated by dispersion corrected DFT method. The predicted interaction energies by MFCC at each computational level are found to give excellent agreement with full system (FS) calculations with the mean energy deviation just a fractional kcal/mol. The accurate determination of nanomaterial-ligand interaction energies by MFCC suggests that it is an effective method for performing QM calculations on nanomaterial-ligand systems.
Zhang, Dawei
2017-01-01
Molecular fractionation with conjugate caps (MFCC) method is introduced for the efficient estimation of quantum mechanical (QM) interaction energies between nanomaterial (carbon nanotube, fullerene, and graphene surface) and ligand (charged and neutral). In the calculations, nanomaterials are partitioned into small fragments and conjugated caps that are properly capped, and the interaction energies can be obtained through the summation of QM calculations of the fragments from which the contribution of the conjugated caps is removed. All the calculations were performed by density functional theory (DFT) and dispersion contributions for the attractive interactions were investigated by dispersion corrected DFT method. The predicted interaction energies by MFCC at each computational level are found to give excellent agreement with full system (FS) calculations with the mean energy deviation just a fractional kcal/mol. The accurate determination of nanomaterial-ligand interaction energies by MFCC suggests that it is an effective method for performing QM calculations on nanomaterial-ligand systems. PMID:28300179
Dai, Peng; Jiang, Nan; Tan, Ren-Xiang
2016-01-01
Elucidation of absolute configuration of chiral molecules including structurally complex natural products remains a challenging problem in organic chemistry. A reliable method for assigning the absolute stereostructure is to combine the experimental circular dichroism (CD) techniques such as electronic and vibrational CD (ECD and VCD), with quantum mechanics (QM) ECD and VCD calculations. The traditional QM methods as well as their continuing developments make them more applicable with accuracy. Taking some chiral natural products with diverse conformations as examples, this review describes the basic concepts and new developments of QM approaches for ECD and VCD calculations in solution and solid states.
Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory
Sun, Yan; Kouri, Donald J.; Truhlar, Donald G.; Schwenke, David W.
1990-01-01
New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.
Institute of Scientific and Technical Information of China (English)
Ge Yu-Cheng
2008-01-01
This paper calculates quantum-mechanically the photoelectron energy spectra excited by attosecond x-rays in the presence of a few-cycle laser. A photoelectron laser phase determination method is used for precise measurements of the pulse natural properties of x-ray intensity and the instantaneous frequency profiles. As a direct procedure without any previous pulse profile assumptions and time-resolved measurements as well as data fitting analysis, this method can be used to improve the time resolutions of attosecond timing and measurements with metrological precision. The measurement range is half of a laser optical cycle.
Superiority of semiclassical over quantum mechanical calculations for a three-dimensional system
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Main, Joerg; Wunner, Guenter; Atilgan, Erdinc; Taylor, Howard S.; Dando, Paul A
2002-12-02
In systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods. However, this situation can be reversed with increasing dimension of the problem. For a three-dimensional system, viz. the hyperbolic four-sphere scattering system, we demonstrate the superiority of semiclassical versus quantum calculations. Semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques.
Superiority of semiclassical over quantum mechanical calculations for a three-dimensional system
Main, Jörg; Wunner, Günter; Atılgan, Erdinç; Taylor, Howard S.; Dando, Paul A.
2002-12-01
In systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods. However, this situation can be reversed with increasing dimension of the problem. For a three-dimensional system, viz. the hyperbolic four-sphere scattering system, we demonstrate the superiority of semiclassical versus quantum calculations. Semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques.
Finkelstein, Noah; Hoehn, Jessica
2017-01-01
Learning quantum mechanics requires students to develop not only new mathematical skills and conceptual understanding, but also has students reason about what these mean and how to organize understanding of quantum mechanical principles, tools and concepts. Towards this instructional goal, we present current research that examines how students make interpretations, probes understanding of student ontologies, and curricula that explicitly addresses interpretation of quantum phenomena and student reasoning structures (ontologies).
Rae, Alastair I M
2016-01-01
A Thorough Update of One of the Most Highly Regarded Textbooks on Quantum Mechanics Continuing to offer an exceptionally clear, up-to-date treatment of the subject, Quantum Mechanics, Sixth Edition explains the concepts of quantum mechanics for undergraduate students in physics and related disciplines and provides the foundation necessary for other specialized courses. This sixth edition builds on its highly praised predecessors to make the text even more accessible to a wider audience. It is now divided into five parts that separately cover broad topics suitable for any general course on quantum mechanics. New to the Sixth Edition * Three chapters that review prerequisite physics and mathematics, laying out the notation, formalism, and physical basis necessary for the rest of the book * Short descriptions of numerous applications relevant to the physics discussed, giving students a brief look at what quantum mechanics has made possible industrially and scientifically * Additional end-of-chapter problems with...
First principles calculation of thermo-mechanical properties of thoria using Quantum ESPRESSO
Malakkal, Linu; Szpunar, Barbara; Zuniga, Juan Carlos; Siripurapu, Ravi Kiran; Szpunar, Jerzy A.
2016-05-01
In this work, we have used Quantum ESPRESSO (QE), an open source first principles code, based on density-functional theory, plane waves, and pseudopotentials, along with quasi-harmonic approximation (QHA) to calculate the thermo-mechanical properties of thorium dioxide (ThO2). Using Python programming language, our group developed qe-nipy-advanced, an interface to QE, which can evaluate the structural and thermo-mechanical properties of materials. We predicted the phonon contribution to thermal conductivity (kL) using the Slack model. We performed the calculations within local density approximation (LDA) and generalized gradient approximation (GGA) with the recently proposed version for solids (PBEsol). We employed a Monkhorst-Pack 5 × 5 × 5 k-points mesh in reciprocal space with a plane wave cut-off energy of 150 Ry to obtain the convergence of the structure. We calculated the dynamical matrices of the lattice on a 4 × 4 × 4 mesh. We have predicted the heat capacity, thermal expansion and the phonon contribution to thermal conductivity, as a function of temperature up to 1400K, and compared them with the previous work and known experimental results.
Evaluation of carbohydrate molecular mechanical force fields by quantum mechanical calculations
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Hemmingsen, Lars Bo Stegeager; Madsen, D.E.; Esbensen, A.L.
2004-01-01
A quantitative evaluation of 20 second-generation carbohydrate force fields was carried out using ab initio and density functional methods. Geometry-optimized structures (B3LYP/6-31G(d)) and relative energies using augmented correlation consistent basis sets were calculated in gas phase...... for monosaccharide carbohydrate benchmark systems. Selected results are: (i) The interaction energy of the alpha-D-alucopyranose-H2O heterodimer is estimated to be 4.9 kcal/mol, using a composite method including terms at highly correlated (CCSD(T)) level. Most molecular mechanics force fields are in error......-generation carbohydrate force fields. No single force field is consistently better than the others for all the test cases. A statistical assessment of the performance of the force fields indicates that CHEAT(95), CFF, certain versions of Amber and of MM3 have the best overall performance, for these gas phase...
A set of molecular models based on quantum mechanical ab initio calculations and thermodynamic data
Eckl, Bernhard; Hasse, Hans
2009-01-01
A parameterization strategy for molecular models on the basis of force fields is proposed, which allows a rapid development of models for small molecules by using results from quantum mechanical (QM) ab initio calculations and thermodynamic data. The geometry of the molecular models is specified according to the atom positions determined by QM energy minimization. The electrostatic interactions are modeled by reducing the electron density distribution to point dipoles and point quadrupoles located in the center of mass of the molecules. Dispersive and repulsive interactions are described by Lennard-Jones sites, for which the parameters are iteratively optimized to experimental vapor-liquid equilibrium (VLE) data, i.e. vapor pressure, saturated liquid density, and enthalpy of vaporization of the considered substance. The proposed modeling strategy was applied to a sample set of ten molecules from different substance classes. New molecular models are presented for iso-butane, cyclohexane, formaldehyde, dimethyl...
Quantum-mechanical calculations of cross sections for electron collisions with atoms and molecules
Bartschat, Klaus; Zatsarinny, Oleg
2016-01-01
An overview of quantum-mechanical methods to generate cross-section data for electron collisions with atoms and molecules is presented. Particular emphasis is placed on the time-independent close-coupling approach, since it is particularly suitable for low-energy collisions and also allows for systematic improvements as well as uncertainty estimates. The basic ideas are illustrated with examples for electron collisions with argon atoms and methane. For many atomic systems, such as e-Ar collisions, highly reliable cross sections can now be computed with quantified uncertainties. On the other hand, while electron collision calculations with molecules do provide key input data for plasma models, the methods and computer codes presently used require further development to make these inputs robust.
Directory of Open Access Journals (Sweden)
Dwyer Donard S
2005-08-01
Full Text Available Abstract Background Electronic properties of amino acid side chains such as inductive and field effects have not been characterized in any detail. Quantum mechanics (QM calculations and fundamental equations that account for substituent effects may provide insight into these important properties. PM3 analysis of electron distribution and polarizability was used to derive quantitative scales that describe steric factors, inductive effects, resonance effects, and field effects of amino acid side chains. Results These studies revealed that: (1 different semiempirical QM methods yield similar results for the electronic effects of side chain groups, (2 polarizability, which reflects molecular deformability, represents steric factors in electronic terms, and (3 inductive effects contribute to the propensity of an amino acid for α-helices. Conclusion The data provide initial characterization of the substituent effects of amino acid side chains and suggest that these properties affect electron density along the peptide backbone.
Zou, Yi; Wang, Fang; Wang, Yan; Guo, Wenjie; Zhang, Yihua; Xu, Qiang; Lai, Yisheng
2017-03-14
Indoleamine 2,3-dioxygenase 1 (IDO1) is regarded as an attractive target for cancer immunotherapy. To rationalize the detailed interactions between IDO1 and its inhibitors at the atomic level, an integrated computational approach by combining molecular mechanics and quantum mechanics methods was employed in this report. Specifically, the binding modes of 20 inhibitors was initially investigated using the induced fit docking (IFD) protocol, which outperformed other two docking protocols in terms of correctly predicting ligand conformations. Secondly, molecular dynamics (MD) simulations and MM/PBSA free energy calculations were employed to determine the dynamic binding process and crucial residues were confirmed through close contact analysis, hydrogen-bond analysis and binding free energy decomposition calculations. Subsequent quantum mechanics and nonbonding interaction analysis were carried out to provide in-depth explanations on the critical role of those key residues, and Arg231 and 7-propionate of the heme group were major contributors to ligand binding, which lowed a great amount of interaction energy. We anticipate that these findings will be valuable for enzymatic studies and rational drug design.
Powell, John L
2015-01-01
Suitable for advanced undergraduates, this thorough text focuses on the role of symmetry operations and the essentially algebraic structure of quantum-mechanical theory. Based on courses in quantum mechanics taught by the authors, the treatment provides numerous problems that require applications of theory and serve to supplement the textual material.Starting with a historical introduction to the origins of quantum theory, the book advances to discussions of the foundations of wave mechanics, wave packets and the uncertainty principle, and an examination of the Schrödinger equation that includ
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Jha Prashant
2009-08-01
Full Text Available Abstract Background Quantum mechanical calculations were performed on a variety of uranium species representing U(VI, U(V, U(IV, U-carbonates, U-phosphates, U-oxalates, U-catecholates, U-phosphodiesters, U-phosphorylated N-acetyl-glucosamine (NAG, and U-2-Keto-3-doxyoctanoate (KDO with explicit solvation by H2O molecules. These models represent major U species in natural waters and complexes on bacterial surfaces. The model results are compared to observed EXAFS, IR, Raman and NMR spectra. Results Agreement between experiment and theory is acceptable in most cases, and the reasons for discrepancies are discussed. Calculated Gibbs free energies are used to constrain which configurations are most likely to be stable under circumneutral pH conditions. Reduction of U(VI to U(IV is examined for the U-carbonate and U-catechol complexes. Conclusion Results on the potential energy differences between U(V- and U(IV-carbonate complexes suggest that the cause of slower disproportionation in this system is electrostatic repulsion between UO2 [CO3]35- ions that must approach one another to form U(VI and U(IV rather than a change in thermodynamic stability. Calculations on U-catechol species are consistent with the observation that UO22+ can oxidize catechol and form quinone-like species. In addition, outer-sphere complexation is predicted to be the most stable for U-catechol interactions based on calculated energies and comparison to 13C NMR spectra. Outer-sphere complexes (i.e., ion pairs bridged by water molecules are predicted to be comparable in Gibbs free energy to inner-sphere complexes for a model carboxylic acid. Complexation of uranyl to phosphorus-containing groups in extracellular polymeric substances is predicted to favor phosphonate groups, such as that found in phosphorylated NAG, rather than phosphodiesters, such as those in nucleic acids.
Mondal, Abhisek; Datta, Saumen
2017-06-01
Hydrogen bond plays a unique role in governing macromolecular interactions with exquisite specificity. These interactions govern the fundamental biological processes like protein folding, enzymatic catalysis, molecular recognition. Despite extensive research work, till date there is no proper report available about the hydrogen bond's energy surface with respect to its geometric parameters, directly derived from proteins. Herein, we have deciphered the potential energy landscape of hydrogen bond directly from the macromolecular coordinates obtained from Protein Data Bank using quantum mechanical electronic structure calculations. The findings unravel the hydrogen bonding energies of proteins in parametric space. These data can be used to understand the energies of such directional interactions involved in biological molecules. Quantitative characterization has also been performed using Shannon entropic calculations for atoms participating in hydrogen bond. Collectively, our results constitute an improved way of understanding hydrogen bond energies in case of proteins and complement the knowledge-based potential. Proteins 2017; 85:1046-1055. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Mandl, F.
1992-07-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Quantum Mechanics aims to teach those parts of the subject which every physicist should know. The object is to display the inherent structure of quantum mechanics, concentrating on general principles and on methods of wide applicability without taking them to their full generality. This book will equip students to follow quantum-mechanical arguments in books and scientific papers, and to cope with simple cases. To bring the subject to life, the theory is applied to the all-important field of atomic physics. No prior knowledge of quantum mechanics is assumed. However, it would help most readers to have met some elementary wave mechanics before. Primarily written for students, it should also be of interest to experimental research workers who require a good grasp of quantum mechanics without the full formalism needed by the professional theorist. Quantum Mechanics features: A flow diagram allowing topics to be studied in different orders or omitted altogether. Optional "starred" and highlighted sections containing more advanced and specialized material for the more ambitious reader. Sets of problems at the end of each chapter to help student understanding. Hints and solutions to the problems are given at the end of the book.
Baulieu, L.; Toppan, Francesco
2016-11-01
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang-Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
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L. Baulieu
2016-11-01
Full Text Available We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang–Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al. and condensed matter properties (Kane et al., where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Energy Technology Data Exchange (ETDEWEB)
Baulieu, L., E-mail: baulieu@lpthe.jussieu.fr [LPTHE – Sorbonne Universités, UPMC, 4 Place Jussieu, 75 005 Paris (France); Toppan, Francesco [CBPF, Rio de Janeiro, Rua Dr. Xavier Sigaud 150, Urca, cep 22290-180 (RJ) (Brazil)
2016-11-15
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang–Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Baulieu, Laurent
2016-01-01
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang-Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories of effective models are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Partition of unity finite element method for quantum mechanical materials calculations
Pask, John E
2016-01-01
The current state of the art for large-scale quantum-mechanical simulations is the planewave (PW) pseudopotential method, as implemented in codes such as VASP, ABINIT, and many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as first-row and transition-metal atoms, and requires significant nonlocal communications, which limit parallel efficiency. Real-space methods such as finite-differences and finite-elements have partially addressed both resolution and parallel-communications issues but have been plagued by one key disadvantage relative to PW: excessive number of degrees of freedom needed to achieve the required accuracies. We present a real-space partition of unity finite element (PUFE) method to solve the Kohn-Sham equations of density functional theory. In the PUFE method, we build the known atomic physics into the solution proc...
On the Systematic Error in the Quantum Mechanical Calculations to the Periodic Table of Elements
Khazan, Albert
2011-05-01
The scientists working on the problems of the Periodic Table of Elements regularly attempt to create models of the elements on the basis of the laws of Quantum Mechanics. One even attempted to use the calculation of the dependency ``atomic mass - element's number'' on this basis, in order to extend the Table by introducing two new Periods containing 50 elements each. The hyperbolic law we have found in the Periodic Table allows to find, first, the atomic mass of the last (heaviest stable) element (411.66), then - the number of the protons in it (155). Two functions were compared: the IUPAC 2007 function (elements 80-118) and another one created according the other data (elements 80-224). Both functions have a large deviation of data in No.104-118. Commencing in Period 8, there are three ``shifts'' of atomic mass for 17, 20, and 25 AMU. Also, our analysis manifests that there in all the aforementioned data is a single point with atomic mass 412 and number 155, where the parameters meet each other. This fact verifies our theory (Khazan A. Upper Limit in Mendeleev's Periodic Table - Element No.155. 2nd ed., Svenska fysikarkivet, Stockholm, 2010).
Fitzpatrick, Richard
2015-01-01
Quantum mechanics was developed during the first few decades of the twentieth century via a series of inspired guesses made by various physicists, including Planck, Einstein, Bohr, Schroedinger, Heisenberg, Pauli, and Dirac. All these scientists were trying to construct a self-consistent theory of microscopic dynamics that was compatible with experimental observations. The purpose of this book is to present quantum mechanics in a clear, concise, and systematic fashion, starting from the fundamental postulates, and developing the theory in as logical manner as possible. Topics covered in the book include the fundamental postulates of quantum mechanics, angular momentum, time-dependent and time-dependent perturbation theory, scattering theory, identical particles, and relativistic electron theory.
Ghosh, P K
2014-01-01
Quantum mechanics, designed for advanced undergraduate and graduate students of physics, mathematics and chemistry, provides a concise yet self-contained introduction to the formal framework of quantum mechanics, its application to physical problems and the interpretation of the theory. Starting with a review of some of the necessary mathematics, the basic concepts are carefully developed in the text. After building a general formalism, detailed treatment of the standard material - the harmonic oscillator, the hydrogen atom, angular momentum theory, symmetry transformations, approximation methods, identical particle and many-particle systems, and scattering theory - is presented. The concluding chapter discusses the interpretation of quantum mechanics. Some of the important topics discussed in the book are the rigged Hilbert space, deformation quantization, path integrals, coherent states, geometric phases, decoherene, etc. This book is characterized by clarity and coherence of presentation.
Molecular dynamics simulation and quantum mechanical calculations on α-D-N-acetylneuraminic acid.
Priyadarzini, Thanu R K; Subashini, Balakrishnan; Selvin, Jeyasigamani F A; Veluraja, Kasinadar
2012-04-01
N-Acetylneuraminic acid is a sugar molecule of biological significance due to its pivotal role in molecular recognition processes. The three dimensional structure and conformation of α-Neu5Ac in biological environments can be clearly observed by molecular dynamics (MD) simulation and quantum mechanical (QM) calculations. A 10ns MD simulation on α-Neu5Ac yields two conformational models which are stabilized by water mediated hydrogen bond between O-8/O-9 hydroxyl oxygen and carbonyl of carboxylate group. The average life time of the conformers and the residual time of water which mediates the hydrogen bonding interactions are computed. Based on the amphiprotic nature of water, water mediation of each conformer is divided into two different modes, one donor-one acceptor mode and two donor modes. According to the analysis of simulation trajectories, the preferred mode of water mediation for conformers is the one donor-one acceptor mode. The energy and geometry of the MD derived conformational models of α-Neu5Ac are optimized using HF/6-31G(∗) basis set of Gaussian03. QM calculations also resulted that α-Neu5Ac is preferentially stabilized by water mediated hydrogen bonding between O-8 hydroxyl and the carboxylate group where the mediation is one donor-one acceptor type. The optimized geometry of α-Neu5Ac which is in good agreement with the crystal structure of α-D-N-acetyl-1-O-methylneuraminic acid methyl ester is deposited in the public domain database 3DSDSCAR (http://3dsdscar.org). This optimized structure can be used by biotechnologists, biophysicists and glycobiologists for modelling the sialylglycans and also to design drugs using sialic acid analog inhibitors. Copyright © 2012 Elsevier Ltd. All rights reserved.
Liu, Peng; Li, Chen; Wang, Dunyou
2017-09-25
The Cl(-) + CH3I → CH3Cl + I(-) reaction in water was studied using combined multi-level quantum mechanism theories and molecular mechanics with an explicit water solvent model. The study shows a significant influence of aqueous solution on the structures of the stationary points along the reaction pathway. A detailed, atomic-level evolution of the reaction mechanism shows a concerted one-bond-broken and one-bond-formed mechanism, as well as a synchronized charge-transfer process. The potentials of mean force calculations with the CCSD(T) and DFT treatments of the solute produce a free activation barrier at 24.5 kcal/mol and 19.0 kcal/mol respectively, which agrees with the experimental one at 22.0 kcal/mol. The solvent effects have also been quantitatively analyzed: in total, the solvent effects raise the activation energy by 20.2 kcal/mol, which shows a significant impact on this reaction in water.
Itoyama, Shuhei; Doitomi, Kazuki; Kamachi, Takashi; Shiota, Yoshihito; Yoshizawa, Kazunari
2016-03-21
Enzymatic methane hydroxylation is proposed to efficiently occur at the dinuclear copper site of particulate methane monooxygenase (pMMO), which is an integral membrane metalloenzyme in methanotrophic bacteria. The resting state and a possible peroxo state of the dicopper active site of pMMO are discussed by using combined quantum mechanics and molecular mechanics calculations on the basis of reported X-ray crystal structures of the resting state of pMMO by Rosenzweig and co-workers. The dicopper site has a unique structure, in which one copper is coordinated by two histidine imidazoles and another is chelated by a histidine imidazole and primary amine of an N-terminal histidine. The resting state of the dicopper site is assignable to the mixed-valent Cu(I)Cu(II) state from a computed Cu-Cu distance of 2.62 Å from calculations at the B3LYP-D/TZVP level of theory. A μ-η(2):η(2)-peroxo-Cu(II)2 structure similar to those of hemocyanin and tyrosinase is reasonably obtained by using the resting state structure and dioxygen. Computed Cu-Cu and O-O distances are 3.63 and 1.46 Å, respectively, in the open-shell singlet state. Structural features of the dicopper peroxo species of pMMO are compared with those of hemocyanin and tyrosinase and synthetic dicopper model compounds. Optical features of the μ-η(2):η(2)-peroxo-Cu(II)2 state are calculated and analyzed with TD-DFT calculations.
Rae, Alastair I M
2007-01-01
PREFACESINTRODUCTION The Photoelectric Effect The Compton Effect Line Spectra and Atomic Structure De Broglie Waves Wave-Particle Duality The Rest of This Book THE ONE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Time-Dependent Schrödinger Equation The Time-Independent Schrödinger Equation Boundary ConditionsThe Infinite Square Well The Finite Square Well Quantum Mechanical Tunneling The Harmonic Oscillator THE THREE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Wave Equations Separation in Cartesian Coordinates Separation in Spherical Polar Coordinates The Hydrogenic Atom THE BASIC POSTULATES OF QUANTUM MEC
Zagoskin, Alexandre
2015-01-01
Written by Dr Alexandre Zagoskin, who is a Reader at Loughborough University, Quantum Mechanics: A Complete Introduction is designed to give you everything you need to succeed, all in one place. It covers the key areas that students are expected to be confident in, outlining the basics in clear jargon-free English, and then providing added-value features like summaries of key ideas, and even lists of questions you might be asked in your exam. The book uses a structure that is designed to make quantum physics as accessible as possible - by starting with its similarities to Newtonian physics, ra
Yang, Zaixing; Wang, Zhigang; Tian, Xingling; Xiu, Peng; Zhou, Ruhong
2012-01-01
Understanding the interaction between carbon nanotubes (CNTs) and biomolecules is essential to the CNT-based nanotechnology and biotechnology. Some recent experiments have suggested that the π-π stacking interactions between protein's aromatic residues and CNTs might play a key role in their binding, which raises interest in large scale modeling of protein-CNT complexes and associated π-π interactions at atomic detail. However, there is concern on the accuracy of classical fixed-charge molecular force fields due to their classical treatments and lack of polarizability. Here, we study the binding of three aromatic residue analogues (mimicking phenylalanine, tyrosine, and tryptophan) and benzene to a single-walled CNT, and compare the molecular mechanical (MM) calculations using three popular fixed-charge force fields (OPLSAA, AMBER, and CHARMM), with quantum mechanical (QM) calculations using the density-functional tight-binding method with the inclusion of dispersion correction (DFTB-D). Two typical configurations commonly found in π-π interactions are used, one with the aromatic rings parallel to the CNT surface (flat), and the other perpendicular (edge). Our calculations reveal that compared to the QM results the MM approaches can appropriately reproduce the strength of π-π interactions for both configurations, and more importantly, the energy difference between them, indicating that the various contributions to π-π interactions have been implicitly included in the van der Waals parameters of the standard MM force fields. Meanwhile, these MM models are less accurate in predicting the exact structural binding patterns (matching surface), meaning there are still rooms to be improved. In addition, we have provided a comprehensive and reliable QM picture for the π-π interactions of aromatic molecules with CNTs in gas phase, which might be used as a benchmark for future force field developments.
Dirac, Paul A M
2001-01-01
The author of this concise, brilliant series of lectures on mathematical methods in quantum mechanics was one of the shining intellects in the field, winning a Nobel prize in 1933 for his pioneering work in the quantum mechanics of the atom. Beyond that, he developed the transformation theory of quantum mechanics (which made it possible to calculate the statistical distribution of certain variables), was one of the major authors of the quantum theory of radiation, codiscovered the Fermi-Dirac statistics, and predicted the existence of the positron.The four lectures in this book were delivered
Jayatilaka, Dylan; Dittrich, Birger
2008-05-01
An approach is outlined for X-ray structure refinement using atomic density fragments obtained by Hirshfeld partitioning of quantum-mechanical density fragments. Results are presented for crystal structure refinements of urea and benzene using these 'Hirshfeld atoms'. Using this procedure, the quantum-mechanical non-spherical electron density is taken into account in the structural model based on the conformation found in the crystal. Contrary to current consensus in structure refinement, the anisotropic displacement parameters of H atoms can be reproduced from neutron diffraction measurements simply from a least-squares fit using the Hirshfeld atoms derived from the BLYP level of theory and including a simple point-charge model to treat the crystal environment.
Li, Hui; Gordon, Mark S
2007-03-28
A method that combines quantum mechanics (QM), typically a solute, the effective fragment potential (EFP) discrete solvent model, and the polarizable continuum model is described. The EFP induced dipoles and polarizable continuum model (PCM) induced surface charges are determined in a self-consistent fashion. The gradients of these two energies with respect to molecular coordinate changes are derived and implemented. In general, the gradients can be formulated as simple electrostatic forces and torques among the QM nuclei, electrons, EFP static multipoles, induced dipoles, and PCM induced charges. Molecular geometry optimizations can be performed efficiently with these gradients. The formulas derived for EFPPCM can be generally applied to other combined molecular mechanics and continuum methods that employ induced dipoles and charges.
Mandl, Franz
1992-01-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scient
Tilborg, Anaëlle; Jacquemin, Denis; Norberg, Bernadette; Perpète, Eric; Michaux, Catherine; Wouters, Johan
2011-12-01
Pharmaceutical compounds are mostly developed as solid dosage forms containing a single-crystal form. It means that the selection of a particular crystal state for a given molecule is an important step for further clinical outlooks. In this context, piracetam, a pharmaceutical molecule known since the sixties for its nootropic properties, is considered in the present work. This molecule is analyzed using several experimental and theoretical approaches. First, the conformational space of the molecule has been systematically explored by performing a quantum mechanics scan of the two most relevant dihedral angles of the lateral chain. The predicted stable conformations have been compared to all the reported experimental geometries retrieved from the Cambridge Structural Database (CSD) covering polymorphs and cocrystals structures. In parallel, different batches of powders have been recrystallized. Under specific conditions, single crystals of polymorph (III) of piracetam have been obtained, an outcome confirmed by crystallographic analysis. © 2011 International Union of Crystallography. Printed in Singapore – all rights reserved.
Sgrignani, Jacopo; Grazioso, Giovanni; De Amici, Marco
2016-09-13
The fast and constant development of drug resistant bacteria represents a serious medical emergency. To overcome this problem, the development of drugs with new structures and modes of action is urgently needed. In this work, we investigated, at the atomistic level, the mechanisms of hydrolysis of Meropenem by OXA-23, a class D β-lactamase, combining unbiased classical molecular dynamics and umbrella sampling simulations with classical force field-based and quantum mechanics/molecular mechanics potentials. Our calculations provide a detailed structural and dynamic picture of the molecular steps leading to the formation of the Meropenem-OXA-23 covalent adduct, the subsequent hydrolysis, and the final release of the inactive antibiotic. In this mechanistic framework, the predicted activation energy is in good agreement with experimental kinetic measurements, validating the expected reaction path.
Mechanism of tungsten-dependent acetylene hydratase from quantum chemical calculations
Liao, Rong-Zhen; Yu, Jian-Guo; Himo, Fahmi
2010-01-01
Acetylene hydratase is a tungsten-dependent enzyme that catalyzes the nonredox hydration of acetylene to acetaldehyde. Density functional theory calculations are used to elucidate the reaction mechanism of this enzyme with a large model of the active site devised on the basis of the native X-ray crystal structure. Based on the calculations, we propose a new mechanism in which the acetylene substrate first displaces the W-coordinated water molecule, and then undergoes a nucleophilic attack by the water molecule assisted by an ionized Asp13 residue at the active site. This is followed by proton transfer from Asp13 to the newly formed vinyl anion intermediate. In the subsequent isomerization, Asp13 shuttles a proton from the hydroxyl group of the vinyl alcohol to the α-carbon. Asp13 is thus a key player in the mechanism, but also W is directly involved in the reaction by binding and activating acetylene and providing electrostatic stabilization to the transition states and intermediates. Several other mechanisms are also considered but the energetic barriers are found to be very high, ruling out these possibilities. PMID:21149684
Calculation of the electron two slit experiment using a quantum mechanical variational principle
Energy Technology Data Exchange (ETDEWEB)
Harrison, Alan K. [Los Alamos National Laboratory
2012-04-17
A nonlocal relativistic variational principle (VP) has recently been proposed as an alternative to the Dirac wave equation of standard quantum mechanics. We apply that principle to the electron two-slit experiment. The detection system is modelled as a screen made of atoms, any one of which can be excited by the incident electron, but we avoid restricting the detection mechanism further. The VP is shown to predict that, at the time the electron reaches the screen, its wavefunction will be localized to the neighborhood of a single atom, resulting in a position-type measurement. In an ensemble of such experiments ('identically prepared' except that the initial phase of the wavefunction - the hidden variable in the VP formulation - is sampled over the expected uniform distribution), the distribution of measured positions will reproduce the interference pattern predicted by the Dirac equation. We also demonstrate that with a detection system designed fundamentally to detect the electron's transverse wavelength rather than its position, the VP predicts that one such mode will be detected, that is, a wavelength measurement will result. Finally, it is shown that these results are unchanged in the 'delayed choice' variant of the experiment.
Li, Ying; Chan, Maria K Y; Sankaranarayanan, Subramanian; Rouxb, Benoît
2016-01-01
In molecular dynamics (MD) simulation, force field determines the capability of an individual model in capturing physical and chemistry properties. The method for generating proper parameters of the force field form is the key component for computational research in chemistry, biochemistry, and condensed-phase physics. Our study showed that the feasibility to predict experimental condensed phase properties (i.e., density and heat of vaporization) of methanol through problem specific force field from only quantum chemistry information. To acquire the satisfying parameter sets of the force field, the genetic algorithm (GA) is the main optimization method. For electrostatic potential energy, we optimized both the electrostatic parameters of methanol using the GA method, which leads to low deviations of between the quantum mechanics (QM) calculations and the GA optimized parameters. We optimized the van der Waals (vdW) parameters both using GA and guided GA methods by calibrating interaction energy of various met...
Afifi, Mahmoud S; Farag, Rabei S; Shaaban, Ibrahim A; Wilson, Lee D; Zoghaib, Wajdi M; Mohamed, Tarek A
2013-07-01
The infrared (4000-200 cm(-1)) spectrum for 4-amino-5-pyrimidinecarbonitrile (APC, C5H4N4) was acquired in the solid phase. In addition, the (1)H and (13)C NMR spectra of APC were obtained in DMSO-d6 along with its mass spectrum. Initially, six isomers were hypothesized and then investigated by means of DFT/B3LYP and MP2(full) quantum mechanical calculations using a 6-31G(d) basis set. Moreover, the (1)H and (13)C NMR chemical shifts were predicted using a GIAO approximation at the 6-311+G(d,p) basis set and the B3LYP method with (and without) solvent effects using PCM method. The correlation coefficients showed good agreement between the experimental/theoretical chemical shift values of amino tautomers (1 and 2) rather than the eliminated imino tautomers (3-6), in agreement with the current quantum mechanical calculations. Structures 3-6 are less stable than the amino tautomers (1 and 2) by about 5206-8673 cm(-1) (62.3-103.7 kJ/mol). The MP2(full)/6-31G(d) computational results favor the amino structure 1 with a pyramidal NH2 moiety and calculated real vibrational frequencies, however; structure 2 is considered a transition state owing to the calculated imaginary frequency. It is worth mentioning that, the calculated structural parameters suggest a strong conjugation between the amino nitrogen and pyrimidine ring. Aided by frequency calculations, normal coordinate analysis, force constants and potential energy distributions (PEDs), a complete vibrational assignment for the observed bands is proposed herein. Finally, NH2 internal rotation barriers for the stable non-planar isomer (1) were carried out using MP2(full)/6-31G(d) optimized structural parameters. Our results are discussed herein and compared to structural parameters for similar molecules whenever appropriate.
Energy Technology Data Exchange (ETDEWEB)
Wang, Xianwei [Center for Optics and Optoelectronics Research, College of Science, Zhejiang University of Technology, Hangzhou, Zhejiang 310023 (China); State Key Laboratory of Precision Spectroscopy, Institute of Theoretical and Computational Science, East China Normal University, Shanghai 200062 (China); Zhang, John Z. H.; He, Xiao, E-mail: xiaohe@phy.ecnu.edu.cn [State Key Laboratory of Precision Spectroscopy, Institute of Theoretical and Computational Science, East China Normal University, Shanghai 200062 (China); NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062 (China)
2015-11-14
Recent advance in biophysics has made it possible to directly measure site-specific electric field at internal sites of proteins using molecular probes with C = O or C≡N groups in the context of vibrational Stark effect. These measurements directly probe changes of electric field at specific protein sites due to, e.g., mutation and are very useful in protein design. Computational simulation of the Stark effect based on force fields such as AMBER and OPLS, while providing good insight, shows large errors in comparison to experimental measurement due to inherent difficulties associated with point charge based representation of force fields. In this study, quantum mechanical calculation of protein’s internal electrostatic properties and vibrational Stark shifts was carried out by using electrostatically embedded generalized molecular fractionation with conjugate caps method. Quantum calculated change of mutation-induced electric field and vibrational Stark shift is reported at the internal probing site of enzyme human aldose reductase. The quantum result is in much better agreement with experimental data than those predicted by force fields, underscoring the deficiency of traditional point charge models describing intra-protein electrostatic properties.
Wang, Xianwei; Zhang, John Z H; He, Xiao
2015-11-14
Recent advance in biophysics has made it possible to directly measure site-specific electric field at internal sites of proteins using molecular probes with C = O or C≡N groups in the context of vibrational Stark effect. These measurements directly probe changes of electric field at specific protein sites due to, e.g., mutation and are very useful in protein design. Computational simulation of the Stark effect based on force fields such as AMBER and OPLS, while providing good insight, shows large errors in comparison to experimental measurement due to inherent difficulties associated with point charge based representation of force fields. In this study, quantum mechanical calculation of protein's internal electrostatic properties and vibrational Stark shifts was carried out by using electrostatically embedded generalized molecular fractionation with conjugate caps method. Quantum calculated change of mutation-induced electric field and vibrational Stark shift is reported at the internal probing site of enzyme human aldose reductase. The quantum result is in much better agreement with experimental data than those predicted by force fields, underscoring the deficiency of traditional point charge models describing intra-protein electrostatic properties.
Ferenczy, György G
2013-04-05
The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009, 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self-consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree-Fock-Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self-consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave-function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem.
Shen, Lin; Yang, Weitao
2016-04-12
We developed a new multiresolution method that spans three levels of resolution with quantum mechanical, atomistic molecular mechanical, and coarse-grained models. The resolution-adapted all-atom and coarse-grained water model, in which an all-atom structural description of the entire system is maintained during the simulations, is combined with the ab initio quantum mechanics and molecular mechanics method. We apply this model to calculate the redox potentials of the aqueous ruthenium and iron complexes by using the fractional number of electrons approach and thermodynamic integration simulations. The redox potentials are recovered in excellent accordance with the experimental data. The speed-up of the hybrid all-atom and coarse-grained water model renders it computationally more attractive. The accuracy depends on the hybrid all-atom and coarse-grained water model used in the combined quantum mechanical and molecular mechanical method. We have used another multiresolution model, in which an atomic-level layer of water molecules around redox center is solvated in supramolecular coarse-grained waters for the redox potential calculations. Compared with the experimental data, this alternative multilayer model leads to less accurate results when used with the coarse-grained polarizable MARTINI water or big multipole water model for the coarse-grained layer.
DEFF Research Database (Denmark)
Mattsson, T.R.; Wahnström, G.; Bengtsson, L.
1997-01-01
First-principles density-functional calculations of hydrogen adsorption on the Ni (001) surface have been performed in order to get a better understanding of adsorption and diffusion of hydrogen on metal surfaces. We find good agreement with experiments for the adsorption energy, binding distance...
Bashmakova, N; Zhurakivsky, R; Hovorun, D; Yashchuk, V
2011-01-01
Experimental vibrational spectra (Raman and infrared absorption) of berberine are obtained at room temperature. The vibrational spectra of berberine are calculated by the DFT method at the B3LYP/6-311++G(d,p) level. Based on the correlation between experimental and calculated data, the vibrational spectrum is interpreted in the frequency range of 800-1700 cm-1 in detail. The experimental and calculated spectra of intramolecular vibrations are found to correlate closely
Lonsdale, Richard; Reetz, Manfred T
2015-11-25
Enoate reductases catalyze the reduction of activated C═C bonds with high enantioselectivity. The oxidative half-reaction, which involves the addition of a hydride and a proton to opposite faces of the C═C bond, has been studied for the first time by hybrid quantum mechanics/molecular mechanics (QM/MM). The reduction of 2-cyclohexen-1-one by YqjM from Bacillus subtilis was selected as the model system. Two-dimensional QM/MM (B3LYP-D/OPLS2005) reaction pathways suggest that the hydride and proton are added as distinct steps, with the former step preceding the latter. Furthermore, we present interesting insights into the reactivity of this enzyme, including the weak binding of the substrate in the active site, the role of the two active site histidine residues for polarization of the substrate C═O bond, structural details of the transition states to hydride and proton transfer, and the role of Tyr196 as proton donor. The information presented here will be useful for the future design of enantioselective YqjM mutants for other substrates.
Directory of Open Access Journals (Sweden)
Khazan A.
2010-10-01
Full Text Available It is shown that only the hyperbolic law of the Periodic Table of Elements allows the exact calculation for the atomic masses. The reference data of Periods 8 and 9 manifest a systematic error in the computer software applied to such a calculation (this systematic error increases with the number of the elements in the Table.
Moura, Gustavo L C; Simas, Alfredo M
2012-04-05
In this article, we advance the foundations of a strategy to develop a molecular mechanics method based not on classical mechanics and force fields but entirely on quantum mechanics and localized electron-pair orbitals, which we call quantum molecular mechanics (QMM). Accordingly, we introduce a new manner of calculating Hartree-Fock ab initio wavefunctions of closed shell systems based on variationally preoptimized nonorthogonal electron pair orbitals constructed by linear combinations of basis functions centered on the atoms. QMM is noniterative and requires only one extremely fast inversion of a single sparse matrix to arrive to the one-particle density matrix, to the electron density, and consequently, to the ab initio electrostatic potential around the molecular system, or cluster of molecules. Although QMM neglects the smaller polarization effects due to intermolecular interactions, it fully takes into consideration polarization effects due to the much stronger intramolecular geometry distortions. For the case of methane, we show that QMM was able to reproduce satisfactorily the energetics and polarization effects of all distortions of the molecule along the nine normal modes of vibration, well beyond the harmonic region. We present the first practical applications of the QMM method by examining, in detail, the cases of clusters of helium atoms, hydrogen molecules, methane molecules, as well as one molecule of HeH(+) surrounded by several methane molecules. We finally advance and discuss the potentialities of an exact formula to compute the QMM total energy, in which only two center integrals are involved, provided that the fully optimized electron-pair orbitals are known.
Hybrid theory and calculation of e-N2 scattering. [quantum mechanics - nuclei (nuclear physics)
Chandra, N.; Temkin, A.
1975-01-01
A theory of electron-molecule scattering was developed which was a synthesis of close coupling and adiabatic-nuclei theories. The theory is shown to be a close coupling theory with respect to vibrational degrees of freedom but is a adiabatic-nuclei theory with respect to rotation. It can be applied to any number of partial waves required, and the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential and total) to be calculated. Explicit formulae for all the cross sections are presented.
Spin Description and Calculations in the Landé Interpretation of Quantum Mechanics
Mweene, H V
1999-01-01
We explain the connection between the generalized spin quantities we have recently introduced and standard forms. We show how the calculation of various quantities of interest using these new forms is done. Focusing attention on expectation values, we find that in every case, the standard results can be obtained as special cases arising from new generalized results.
Directory of Open Access Journals (Sweden)
Yuriy Natanzon
2008-01-01
Full Text Available We report ﬁrst principles calculations of the electronic and elastic properties of yttriastabilized tetragonal zirconium dioxide doped with metal oxides like: GeO2, TiO2, SiO2,MgO and Al2O3. It is shown that addition of such dopants aﬀects selected elastic propertiesof ZrO2, which is driven by the attraction of electron density by dopant atom and creationof stronger dopant–oxygen bonds. This eﬀect contributes to the increase of superplasticityof doped material.
Piezo-optic tensor of crystals from quantum-mechanical calculations
Energy Technology Data Exchange (ETDEWEB)
Erba, A., E-mail: alessandro.erba@unito.it; Dovesi, R. [Dipartimento di Chimica, Università di Torino and NIS, Nanostructured Interfaces and Surfaces, Centre of Excellence, Via Giuria 5, 10125 Torino (Italy); Ruggiero, M. T.; Korter, T. M. [Department of Chemistry, Syracuse University, 1-014 Center for Science and Technology, Syracuse, New York 13244-4100 (United States)
2015-10-14
An automated computational strategy is devised for the ab initio determination of the full fourth-rank piezo-optic tensor of crystals belonging to any space group of symmetry. Elastic stiffness and compliance constants are obtained as numerical first derivatives of analytical energy gradients with respect to the strain and photo-elastic constants as numerical derivatives of analytical dielectric tensor components, which are in turn computed through a Coupled-Perturbed-Hartree-Fock/Kohn-Sham approach, with respect to the strain. Both point and translation symmetries are exploited at all steps of the calculation, within the framework of periodic boundary conditions. The scheme is applied to the determination of the full set of ten symmetry-independent piezo-optic constants of calcium tungstate CaWO{sub 4}, which have recently been experimentally reconstructed. Present calculations unambiguously determine the absolute sign (positive) of the π{sub 61} constant, confirm the reliability of 6 out of 10 experimentally determined constants and provide new, more accurate values for the remaining 4 constants.
Piezo-optic tensor of crystals from quantum-mechanical calculations.
Erba, A; Ruggiero, M T; Korter, T M; Dovesi, R
2015-10-14
An automated computational strategy is devised for the ab initio determination of the full fourth-rank piezo-optic tensor of crystals belonging to any space group of symmetry. Elastic stiffness and compliance constants are obtained as numerical first derivatives of analytical energy gradients with respect to the strain and photo-elastic constants as numerical derivatives of analytical dielectric tensor components, which are in turn computed through a Coupled-Perturbed-Hartree-Fock/Kohn-Sham approach, with respect to the strain. Both point and translation symmetries are exploited at all steps of the calculation, within the framework of periodic boundary conditions. The scheme is applied to the determination of the full set of ten symmetry-independent piezo-optic constants of calcium tungstate CaWO4, which have recently been experimentally reconstructed. Present calculations unambiguously determine the absolute sign (positive) of the π61 constant, confirm the reliability of 6 out of 10 experimentally determined constants and provide new, more accurate values for the remaining 4 constants.
Era, Masanao; Yasuda, Takeshi; Mori, Kento; Tomotsu, Norio; Kawano, Naoki; Koshimizu, Masanori; Asai, Keisuke
2016-04-01
We have successfully evaluated hole mobility in a spin-coated film of a lead-bromide based layered perovskite having carbazole chromophore-linked ammonium molecules as organic layer by using FET measurement. The values of hole mobility, threshold voltage and on/off ratio at room temperature were evaluated.to.be 1.7 x 10(-6) cm2 V-1 s-1, 27 V and 28 V, respectively. However, the spin-coated films on Si substrates were not so uniform compared with those on fused quartz substrates. To improve the film uniformity, we examined the relationship between substrate temperature during spin-coating and film morphology in the layered perovskite spin-coated films. The mean roughness of the spin-coated films on Si substrates was dependent on the substrate temperature. At 353 K, the mean roughness was minimized and the carrier mobility was enhanced by one order of magnitude; the values of hole mobility and threshold voltage were .estimated to be 3.4 x 10(-5) cm2 V-1 s-1, and 22 V at room temperature in a preliminary FET evaluation, respectively. In addition, we determined a crystal structure of the layered perovskite by X-ray diffraction analysis. To gain a better understanding of the observed hole transports, we conducted quantum mechanical calculations using the obtained crystal structure information. The calculated band structure of the layered organic perovskite showed that the valence band is composed of the organic carbazole layer, which confirms that.the measured hole mobility is mainly derived from the organic part of the layered perovskite. Band and hopping transport mechanisms were discussed by calculating the effective masses and transfer integrals for the 2D periodic system of the organic layer in isolation.
Legler, C R; Brown, N R; Dunbar, R A; Harness, M D; Nguyen, K; Oyewole, O; Collier, W B
2015-06-15
The Scaled Quantum Mechanical (SQM) method of scaling calculated force constants to predict theoretically calculated vibrational frequencies is expanded to include a broad array of polarized and augmented basis sets based on the split valence 6-31G and 6-311G basis sets with the B3LYP density functional. Pulay's original choice of a single polarized 6-31G(d) basis coupled with a B3LYP functional remains the most computationally economical choice for scaled frequency calculations. But it can be improved upon with additional polarization functions and added diffuse functions for complex molecular systems. The new scale factors for the B3LYP density functional and the 6-31G, 6-31G(d), 6-31G(d,p), 6-31G+(d,p), 6-31G++(d,p), 6-311G, 6-311G(d), 6-311G(d,p), 6-311G+(d,p), 6-311G++(d,p), 6-311G(2d,p), 6-311G++(2d,p), 6-311G++(df,p) basis sets are shown. The double d polarized models did not perform as well and the source of the decreased accuracy was investigated. An alternate system of generating internal coordinates that uses the out-of plane wagging coordinate whenever it is possible; makes vibrational assignments via potential energy distributions more meaningful. Automated software to produce SQM scaled vibrational calculations from different molecular orbital packages is presented.
Ferenczy, György G
2013-04-05
Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods.
Quantum-mechanical calculation of ionization potential lowering in dense plasmas
Son, Sang-Kil; Jurek, Zoltan; Ziaja, Beata; Santra, Robin
2014-01-01
The charged environment within a dense plasma leads to the phenomenon of ionization potential depression (IPD) for ions embedded in the plasma. Accurate predictions of the IPD effect are of crucial importance for modeling atomic processes occurring within dense plasmas. Several theoretical models have been developed to describe the IPD effect, with frequently discrepant predictions. Only recently, first experiments on IPD in Al plasma have been performed with an x-ray free-electron laser (XFEL), where their results were found to be in disagreement with the widely-used IPD model by Stewart and Pyatt. Another experiment on Al, at the Orion laser, showed disagreement with the model by Ecker and Kr\\"oll. This controversy shows a strong need for a rigorous and consistent theoretical approach to calculate the IPD effect. Here we propose such an approach: a two-step Hartree-Fock-Slater model. With this parameter-free model we can accurately and efficiently describe the experimental Al data and validate the accuracy ...
Monari, Antonio; Rivail, Jean-Louis; Assfeld, Xavier
2013-02-19
Molecular mechanics methods can efficiently compute the macroscopic properties of a large molecular system but cannot represent the electronic changes that occur during a chemical reaction or an electronic transition. Quantum mechanical methods can accurately simulate these processes, but they require considerably greater computational resources. Because electronic changes typically occur in a limited part of the system, such as the solute in a molecular solution or the substrate within the active site of enzymatic reactions, researchers can limit the quantum computation to this part of the system. Researchers take into account the influence of the surroundings by embedding this quantum computation into a calculation of the whole system described at the molecular mechanical level, a strategy known as the mixed quantum mechanics/molecular mechanics (QM/MM) approach. The accuracy of this embedding varies according to the types of interactions included, whether they are purely mechanical or classically electrostatic. This embedding can also introduce the induced polarization of the surroundings. The difficulty in QM/MM calculations comes from the splitting of the system into two parts, which requires severing the chemical bonds that link the quantum mechanical subsystem to the classical subsystem. Typically, researchers replace the quantoclassical atoms, those at the boundary between the subsystems, with a monovalent link atom. For example, researchers might add a hydrogen atom when a C-C bond is cut. This Account describes another approach, the Local Self Consistent Field (LSCF), which was developed in our laboratory. LSCF links the quantum mechanical portion of the molecule to the classical portion using a strictly localized bond orbital extracted from a small model molecule for each bond. In this scenario, the quantoclassical atom has an apparent nuclear charge of +1. To achieve correct bond lengths and force constants, we must take into account the inner shell of
Shi, Qicun; Meroueh, Samy O; Fisher, Jed F; Mobashery, Shahriar
2008-07-23
Penicillin-binding protein 5 (PBP 5) of Escherichia coli hydrolyzes the terminal D-Ala-D-Ala peptide bond of the stem peptides of the cell wall peptidoglycan. The mechanism of PBP 5 catalysis of amide bond hydrolysis is initial acylation of an active site serine by the peptide substrate, followed by hydrolytic deacylation of this acyl-enzyme intermediate to complete the turnover. The microscopic events of both the acylation and deacylation half-reactions have not been studied. This absence is addressed here by the use of explicit-solvent molecular dynamics simulations and ONIOM quantum mechanics/molecular mechanics (QM/MM) calculations. The potential-energy surface for the acylation reaction, based on MP2/6-31+G(d) calculations, reveals that Lys47 acts as the general base for proton abstraction from Ser44 in the serine acylation step. A discrete potential-energy minimum for the tetrahedral species is not found. The absence of such a minimum implies a conformational change in the transition state, concomitant with serine addition to the amide carbonyl, so as to enable the nitrogen atom of the scissile bond to accept the proton that is necessary for progression to the acyl-enzyme intermediate. Molecular dynamics simulations indicate that transiently protonated Lys47 is the proton donor in tetrahedral intermediate collapse to the acyl-enzyme species. Two pathways for this proton transfer are observed. One is the direct migration of a proton from Lys47. The second pathway is proton transfer via an intermediary water molecule. Although the energy barriers for the two pathways are similar, more conformers sample the latter pathway. The same water molecule that mediates the Lys47 proton transfer to the nitrogen of the departing D-Ala is well positioned, with respect to the Lys47 amine, to act as the hydrolytic water in the deacylation step. Deacylation occurs with the formation of a tetrahedral intermediate over a 24 kcal x mol(-1) barrier. This barrier is approximately 2
Greiner, Walter
1989-01-01
"Quantum Dynamics" is a major survey of quantum theory based on Walter Greiner's long-running and highly successful courses at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in partic...
Introduction to quantum mechanics
Villaseñor, Eduardo J. S.
2008-01-01
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.
Mishra, H.; Colussi, A. J.; Enami, S.; Nielsen, R. J.; Hoffmann, M. R.; Goddard, W. A.
2012-12-01
It has become increasingly apparent that atmospheric chemistry involves more than gas-phase reactions. Key processes, such as the decay of NO2 in urban plumes and the associated daytime formation of HONO, and the rapid chemistries observed in and over forest canopies at nighttime defy explanation by conventional atmospheric chemistry mechanisms. We have recently reported experimental results on several gas-liquid reactions of atmospheric interest, such as the facile protonation of gaseous isoprene on mildly acidic (pH bioenergetics coupling, 'on-water' catalysis, self-assembly and molecular recognition, little is known about the molecular mechanisms of such reactions. Herein we apply quantum mechanics to investigate how biogenic or anthropogenic olefins may get protonated and undergo oligomerization at the air-water interface by performing model calculations on small water clusters carrying an excess proton as surrogates for the surface of mildly acidic water as sensed by gaseous isoprene (ISO). We find that ISO binds weakly to the surface of water and accepts a proton from H+(H2O)3, leading to ISOH+ via a proton transfer hindered by a ΔG1‡ = 5.6 kcal mol-1 kinetic barrier. Subsequently, another ISO attaches loosely to this ensemble, before being attacked by the ISOH+. This process, which represents the first step of the cationic polymerization of ISO, is hindered by a similar ΔG2‡ = 5.7 kcal mol-1 barrier. Our theoretical results are consistent with experimental (~ 10-4) uptake coefficients for ISO measured on acidic water.
Mullin, Jonathan; Valley, Nicholas; Blaber, Martin G; Schatz, George C
2012-09-27
Multiscale models that combine quantum mechanics and classical electrodynamics are presented, which allow for the evaluation of surface-enhanced Raman (SERS) and hyper-Raman scattering spectra (SEHRS) for both chemical (CHEM) and electrodynamic (EM) enhancement mechanisms. In these models, time-dependent density functional theory (TDDFT) for a system consisting of the adsorbed molecule and a metal cluster fragment of the metal particle is coupled to Mie theory for the metal particle, with the surface of the cluster being overlaid with the surface of the metal particle. In model A, the electromagnetic enhancement from plasmon-excitation of the metal particle is combined with the chemical enhancement associated with a static treatment of the molecule-metal structure to determine overall spectra. In model B, the frequency dependence of the Raman spectrum of the isolated molecule is combined with the enhancements determined in model A to refine the enhancement estimate. An equivalent theory at the level of model A is developed for hyper-Raman spectra calculations. Application to pyridine interacting with a 20 nm diameter silver sphere is presented, including comparisons with an earlier model (denoted G), which combines plasmon enhanced fields with gas-phase Raman (or hyper-Raman) spectra. The EM enhancement factor for spherical particles at 357 nm is found to be 10(4) and 10(6) for SERS and SEHRS, respectively. Including both chemical and electromagnetic mechanisms at the level of model A leads to enhancements on the order of 10(4) and 10(9) for SERS and SEHRS.
Teo, Boon K.; Li, Wai-Kee
2011-01-01
This article is divided into two parts. In the first part, the atomic unit (au) system is introduced and the scales of time, space (length), and speed, as well as those of mass and energy, in the atomic world are discussed. In the second part, the utility of atomic units in quantum mechanical and spectroscopic calculations is illustrated with…
Testing Nonassociative Quantum Mechanics.
Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut
2015-11-27
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
Ahn, Doyeol
2011-01-01
A clear introduction to quantum mechanics concepts Quantum mechanics has become an essential tool for modern engineering, particularly due to the recent developments in quantum computing as well as the rapid progress in optoelectronic devices. Engineering Quantum Mechanics explains the fundamentals of this exciting field, providing broad coverage of both traditional areas such as semiconductor and laser physics as well as relatively new yet fast-growing areas such as quantum computation and quantum information technology. The book begins with basic quantum mechanics, reviewing measurements and probability, Dirac formulation, the uncertainty principle, harmonic oscillator, angular momentum eigenstates, and perturbation theory. Then, quantum statistical mechanics is explored, from second quantization and density operators to coherent and squeezed states, coherent interactions between atoms and fields, and the Jaynes-Cummings model. From there, the book moves into elementary and modern applications, discussing s...
Advanced Visual Quantum Mechanics
Thaller, Bernd
2005-01-01
Advanced Visual Quantum Mechanics is a systematic effort to investigate and to teach quantum mechanics with the aid of computer-generated animations. It is a self-contained textbook that combines selected topics from atomic physics (spherical symmetry, the hydrogen atom, and particles with spin) with an introduction to quantum information theory (qubits, EPR paradox, teleportation, quantum computers). It explores relativistic quantum mechanics and the strange behavior of Dirac equation solutions. A series of appendices covers important topics from perturbation and scattering theory. The book places an emphasis on ideas and concepts, with a fair to moderate amount of mathematical rigor. Though this book stands alone, it can also be paired with Thaller Visual Quantum Mechanics to form a comprehensive course in quantum mechanics. The software for the first book earned the European Academic Software Award 2000 for outstanding innovation in its field.
Rai, Neeraj; Tiwari, Surya P; Maginn, Edward J
2012-09-06
Advances in computational algorithms and methodologies make it possible to use highly accurate quantum mechanical calculations to develop force fields (pair-wise additive intermolecular potentials) for condensed phase simulations. Despite these advances, this approach faces numerous hurdles for the case of actinyl ions, AcO2(n+) (high-oxidation-state actinide dioxo cations), mainly due to the complex electronic structure resulting from an interplay of s, p, d, and f valence orbitals. Traditional methods use a pair of molecules (“dimer”) to generate a potential energy surface (PES) for force field parametrization based on the assumption that many body polarization effects are negligible. We show that this is a poor approximation for aqueous phase uranyl ions and present an alternative approach for the development of actinyl ion force fields that includes important many body solvation effects. Force fields are developed for the UO2(2+) ion with the SPC/Fw, TIP3P, TIP4P, and TIP5P water models and are validated by carrying out detailed molecular simulations on the uranyl aqua ion, one of the most characterized actinide systems. It is shown that the force fields faithfully reproduce available experimental structural data and hydration free energies. Failure to account for solvation effects when generating PES leads to overbinding between UO2(2+) and water, resulting in incorrect hydration free energies and coordination numbers. A detailed analysis of arrangement of water molecules in the first and second solvation shell of UO2(2+) is presented. The use of a simple functional form involving the sum of Lennard-Jones + Coulomb potentials makes the new force field compatible with a large number of available molecular simulation engines and common force fields.
Welch, Mark D.; Montgomery, Wren; Balan, Etienne; Lerch, Philippe
2012-02-01
The high-pressure behavior of Keokuk kaolinite has been studied to 9.5 GPa by infrared spectroscopy using synchrotron radiation. The kaolinite-I → kaolinite-II and kaolinite-II → kaolinite-III transformations have clear spectroscopic expression, with discontinuities coinciding with the transformation pressures bracketed by X-ray diffraction (Welch and Crichton in Am Mineral 95:651-654, 2010). The experimental spectra have been interpreted from band assignments derived from density functional theory for the structures of kaolinite-II and kaolinite-III, using as starting models the ab initio structures reported by Mercier and Le Page (Acta Crystallogr A B64:131-143, 2008, Mater Sci Technol 25:437-442, 2009) and unit-cell parameters from Welch and Crichton (Am Mineral 95:651-654, 2010). The relaxed theoretical structures are very similar to those reported by Mercier and Le Page (Acta Crystallogr A B64:131-143, 2008, Mater Sci Technol 25:437-442, 2009) in their theoretical investigation of kaolinite polytypes at high pressure. The vibrational spectra calculated from the quantum-mechanical analysis allow band assignments of the IR spectra to be made and provide insights into the behavior of different OH environments in the two high-pressure polytypes. The single perpendicular-interlayer OH group of kaolinite-III has a distinctive spectroscopic signature that is diagnostic of this polytype (ν = 3,595 cm-1 at 9.5 GPa) and is sensitive to the compression/expansion of the interlayer space. This OH group also has a distinctive signature in the calculated spectra. The spectra collected on decompression are those of kaolinite-III and persist largely unchanged to 4.6 GPa, except for a continuous blue shift of the 3,595 cm-1 band to 3,613 cm-1. Finally, kaolinite-I is recovered at 0.6 GPa, confirming the kaolinite-III → kaolinite-I transformation previously observed by X-ray diffraction, and the irreversibility of the kaolinite-II → kaolinite-III transformation. The
Quantum mechanics in chemistry
Schatz, George C
2002-01-01
Intended for graduate and advanced undergraduate students, this text explores quantum mechanical techniques from the viewpoint of chemistry and materials science. Dynamics, symmetry, and formalism are emphasized. An initial review of basic concepts from introductory quantum mechanics is followed by chapters examining symmetry, rotations, and angular momentum addition. Chapter 4 introduces the basic formalism of time-dependent quantum mechanics, emphasizing time-dependent perturbation theory and Fermi's golden rule. Chapter 5 sees this formalism applied to the interaction of radiation and matt
Quantum mechanics for pedestrians
Pade, Jochen
2014-01-01
This book provides an introduction into the fundamentals of non-relativistic quantum mechanics. In Part 1, the essential principles are developed. Applications and extensions of the formalism can be found in Part 2. The book includes not only material that is presented in traditional textbooks on quantum mechanics, but also discusses in detail current issues such as interaction-free quantum measurements, neutrino oscillations, various topics in the field of quantum information as well as fundamental problems and epistemological questions, such as the measurement problem, entanglement, Bell's inequality, decoherence, and the realism debate. A chapter on current interpretations of quantum mechanics concludes the book. To develop quickly and clearly the main principles of quantum mechanics and its mathematical formulation, there is a systematic change between wave mechanics and algebraic representation in the first chapters. The required mathematical tools are introduced step by step. Moreover, the appendix coll...
Wei, Donghui; Fang, Lei; Tang, Mingsheng; Zhan, Chang-Guo
2013-10-31
Proteasome is the major component of the crucial non-lysosomal protein degradation pathway in the cells, but the detailed reaction pathway is unclear. In this study, first-principles quantum mechanical/molecular mechanical free energy calculations have been performed to explore, for the first time, possible reaction pathways for proteasomal proteolysis/hydrolysis of a representative peptide, succinyl-leucyl-leucyl-valyl-tyrosyl-7-amino-4-methylcoumarin (Suc-LLVY-AMC). The computational results reveal that the most favorable reaction pathway consists of six steps. The first is a water-assisted proton transfer within proteasome, activating Thr1-O(γ). The second is a nucleophilic attack on the carbonyl carbon of a Tyr residue of substrate by the negatively charged Thr1-O(γ), followed by the dissociation of the amine AMC (third step). The fourth step is a nucleophilic attack on the carbonyl carbon of the Tyr residue of substrate by a water molecule, accompanied by a proton transfer from the water molecule to Thr1-N(z). Then, Suc-LLVY is dissociated (fifth step), and Thr1 is regenerated via a direct proton transfer from Thr1-N(z) to Thr1-O(γ). According to the calculated energetic results, the overall reaction energy barrier of the proteasomal hydrolysis is associated with the transition state (TS3(b)) for the third step involving a water-assisted proton transfer. The determined most favorable reaction pathway and the rate-determining step have provided a reasonable interpretation of the reported experimental observations concerning the substituent and isotopic effects on the kinetics. The calculated overall free energy barrier of 18.2 kcal/mol is close to the experimentally derived activation free energy of ∼18.3-19.4 kcal/mol, suggesting that the computational results are reasonable.
Selg, M
2005-01-01
Elegant and mathematically rigorous methods of the quantum inverse theory are difficult to put into practice because there is always some lack of needful input information. In this situation, one may try to construct a reference potential, whose spectral characteristics would be in a reasonable agreement with the available data of the system's properties. Since the reference potential is fixed, it is always possible to calculate all its spectral characteristics, including phase shift for scattering states and Jost function, the main key to solve the inverse problem. Thereafter, one can calculate a Bargmann potential whose Jost function differs from the initial one only by a rational factor. This way it is possible, at least in principle, to construct a more reliable potential for the system. The model system investigated in this paper is diatomic xenon molecule in ground electronic state. Its reference potential is built up of several smoothly joined Morse type components, which enables to solve the related e...
Facing quantum mechanical reality.
Rohrlich, F
1983-09-23
Two recent precision experiments provide conclusive evidence against any local hidden variables theory and in favor of standard quantum mechanics. Therefore the epistemology and the ontology of quantum mechanics must now be taken more seriously than ever before. The consequences of the standard interpretation of quantum mechanics are summarized in nontechnical language. The implications of the finiteness of Planck's constant (h > 0) for the quantum world are as strange as the implications of the finiteness of the speed of light (c < infinity for space and time in relativity theory. Both lead to realities beyond our common experience that cannot be rejected.
Holography and Quantum Mechanics
Wang, X J
2002-01-01
It is illustrated that quantum mechanics can be interpreted as holographic projection of higher dimension classical gravity. In this explanation every quantum path in D-dimension is dual to a classical path of (D+1)-dimension gravity under definite holographic projection. I consider 2-dimension non-relativitic free particle and harmonic oscillator as two examples, and find their gravity dual. I conjecture that every quantum mechanics system has their dual gravity description.
Elementary Nonrelativistic Quantum Mechanics
Rosu, H C
2000-01-01
This is a graduate course on elementary quantum mechanics written for the benefit of undergraduate and graduate students. It is the English version of physics/0003106, which I did at the suggestion of several students from different countries. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum and spin, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
Gol'dman, I I
2010-01-01
A comprehensive collection of problems of varying degrees of difficulty in nonrelativistic quantum mechanics, with answers and completely worked-out solutions. Among the topics: one-dimensional motion, transmission through a potential barrier, commutation relations, angular momentum and spin, and motion of a particle in a magnetic field. An ideal adjunct to any textbook in quantum mechanics, useful in courses in atomic and nuclear physics, mathematical methods in physics, quantum statistics and applied differential equations. 1961 edition.
Pirojsirikul, Teerapong; Götz, Andreas W; Weare, John; Walker, Ross C; Kowalski, Karol; Valiev, Marat
2017-07-05
Combined quantum mechanical molecular mechanics (QM/MM) calculations have become a popular methodology for efficient and accurate description of large molecular systems. In this work we introduce our development of a QM/MM framework based on two well-known codes-NWChem and AMBER. As an initial application area we are focused on excited state properties of small molecules in an aqueous phase using an analogue of the green fluorescent protein (GFP) chromophore as a particular test case. Our approach incorporates high level coupled cluster theory for the analysis of excited states providing a reliable theoretical analysis of effects of an aqueous solvation environment on the photochemical properties of the GFP chromophore. Using a systematic approach, which involves comparison of gas phase and aqueous phase results for different protonation states and conformations, we resolve existing uncertainties regarding the theoretical interpretation of experimental data. We observe that the impact of aqueous environment on charged states generally results in blue shifts of the absorption spectra, but the magnitude of the effect is sensitive to both protonation state and conformation and can be rationalized based on charge movement into the area of higher/lower external electrostatic potentials. At neutral pH levels the experimentally observed absorption signal is most likely coming from the phenol protonated form. Our results also show that the high level electron correlated method is essential for a proper description of excited states of GFP. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu
2012-01-01
We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.
Goldman, Iosif Ilich; Geilikman, B T
2006-01-01
This challenging book contains a comprehensive collection of problems in nonrelativistic quantum mechanics of varying degrees of difficulty. It features answers and completely worked-out solutions to each problem. Geared toward advanced undergraduates and graduate students, it provides an ideal adjunct to any textbook in quantum mechanics.
Directory of Open Access Journals (Sweden)
Tadashi Okazaki
2015-01-01
Full Text Available We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the BLG-model and the ABJM-model compactified on a torus are N=16 and N=12 superconformal gauged quantum mechanics. After integrating out the auxiliary gauge fields we find OSp(16|2 and SU(1,1|6 quantum mechanics from the reduced systems. The curved Riemann surface is taken as a holomorphic curve in a Calabi–Yau space to preserve supersymmetry and we present a prescription of the topological twisting. We find the N=8 superconformal gauged quantum mechanics that may describe the motion of two wrapped M2-branes in a K3 surface.
Pitari, Fabio; Bovi, Daniele; Narzi, Daniele; Guidoni, Leonardo
2015-09-29
The Mn4CaO5 cluster in the oxygen-evolving complex is the catalytic core of the Photosystem II (PSII) enzyme, responsible for the water splitting reaction in oxygenic photosynthesis. The role of the redox-inactive ion in the cluster has not yet been fully clarified, although several experimental data are available on Ca2+-depleted and Ca2+-substituted PSII complexes, indicating Sr2+-substituted PSII as the only modification that preserves oxygen evolution. In this work, we investigated the structural and electronic properties of the PSII catalytic core with Ca2+ replaced with Sr2+ and Cd2+ in the S2 state of the Kok−Joliot cycle by means of density functional theory and ab initio molecular dynamics based on a quantum mechanics/ molecular mechanics approach. Our calculations do not reveal significant differences between the substituted and wild-type systems in terms of geometries, thermodynamics, and kinetics of two previously identified intermediate states along the S2 to S3 transition, namely, the open cubane S2 A and closed cubane S2 B conformers. Conversely, our calculations show different pKa values for the water molecule bound to the three investigated heterocations. Specifically, for Cd-substituted PSII, the pKa value is 5.3 units smaller than the respective value in wild type Ca-PSII. On the basis of our results, we conclude that, assuming all the cations sharing the same binding site, the induced difference in the acidity of the binding pocket might influence the hydrogen bonding network and the redox levels to prevent the further evolution of the cycle toward the S3 state.
Quantum mechanics of materials
Energy Technology Data Exchange (ETDEWEB)
Cohen, M.L.; Heine, V.; Phillips, J.C.
1982-06-01
In the past 25 years, new quantum-mechanical methods have been developed for predicting the configuration of the valence electrons in an atom or an aggregate of many atoms, within the range of energy excitations in which the atoms form interatomic bonds. A theory specifying the configuration of the valence electrons has much to say about the bulk properties of matter that depends on the nature of the interatomic bonds. The new method regards the core electrons and the atomic nucleus as if they constituted a single particle without internal structure. The method is called the pseudopotential theory. A general quantum-mechanical prediction of the properties of a substance in terms of the additive properties of separate chemical bonds is not yet feasible for molecules. However, there is one realm where prediction is now practical: crystalline solids. The regularity of the lattice into which the atoms are organized in a crystal makes it possible to calculate the properties of a macroscopic solid. In other words, many properties of an elemental solid such as lead or a simple binary solid such as gallium arsenide can not be deduced from energy considerations alone. (SC)
Quantum Mechanics interpreted in Quantum Real Numbers
Corbett, J V; Corbett, John V; Durt, Thomas
2002-01-01
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms of quantum mechanics are re-interpreted. Our aim is to show that, when formulated in the language of quantum real numbers, the laws of quantum mechanics appear more natural, less counterintuitive than when they are presented in terms of standard numbers.
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [California Institute of Technology, Pasadena, California 91125 (United States)
2013-06-15
We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.
Quantum mechanics for mathematicians
Takhtajan, Leon A
2008-01-01
This book provides a comprehensive treatment of quantum mechanics from a mathematics perspective and is accessible to mathematicians starting with second-year graduate students. It addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrodinger equation, this book gives a mathematical treatment of systems of identical particles with spin, and it introduces the reader to functional methods in quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, supersymmetry and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathematicians could find these topics only in physics textbooks ...
Quantum Chaos and Statistical Mechanics
Srednicki, Mark
1994-01-01
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
Jung, Julie; Guennic, Boris Le; Fedin, Matvey V; Ovcharenko, Victor I; Calzado, Carmen J
2015-07-20
The gradual magnetostructural transition in breathing crystals based on copper(II) and pyrazolyl-substituted nitronyl nitroxides has been analyzed by means of DDCI quantum chemistry calculations. The magnetic coupling constants (J) within the spin triads of Cu(hfac)2L(Bu)·0.5C8H18 have been evaluated for the X-ray structures reported at different temperatures. The coupling is strongly antiferromagnetic at low temperature and becomes ferromagnetic when the temperature increases. The intercluster magnetic coupling (J') is antiferromagnetic and shows a marked dependence on temperature. The magnetostructural transition can be reproduced using the calculated J values for each structure in the simulation of the magnetic susceptibility. However, the μ(T) curve can be improved nicely by considering the coexistence of two phases in the transition region, whose ratio varies with temperature corresponding to both the weakly and strongly coupled spin states. These results complement a recent VT-FTIR study on the parent Cu(hfac)2L(Pr) compound with a gradual magnetostructural transition.
Quantum mechanical Carnot engine
Bender, C M; Meister, B K
2000-01-01
A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.
Odake, Satoru; Sasaki, Ryu
2011-01-01
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creati...
Rosu, H C
2000-01-01
This is the first graduate course on elementary quantum mechanics in Internet written in Romanian for the benefit of Romanian speaking students (Romania and Moldova). It is a translation (with corrections) of the Spanish version of the course (physics/9808031, English translation is under consideration), which I did at the request of students of physics in Bucharest. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum and spin, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
Effectively Emergent Quantum Mechanics
Exirifard, Qasem
2008-01-01
We consider non minimal coupling between matters and gravity in modified theories of gravity. In contrary to the current common sense, we report that quantum mechanics can effectively emerge when the space-time geometry is sufficiently flat. In other words, quantum mechanics might play no role when and where the space-time geometry is highly curved. We study the first two simple models of Effectively Emergent Quantum Mechanics(EEQM): R-dependent EEQM and G-dependent EEQM where R is the Ricci scalar and G is the Gauss-Bonnet Lagrangian density. We discuss that these EEQM theories might be fine tuned to remain consistent with all the implemented experiments and performed observations. In particular, we observe that G-dependent EEQM softens the problem of quantum gravity.
Shaltout, I; Mohamed, Tarek A
2007-06-01
Chozen system of tellurite glasses doped with rare earth oxides (95% alpha-TeO(2)+5% Sm2O3) was prepared by melt quenching. Consequently, the Raman spectrum (150-1250 cm(-1)) of the modified tellurite have been recorded. As a continuation to our normal coordinate analysis, force constants and quantum mechanical (QM) calculations for tbp TeO4(4-) (triagonal bipyramid, C(2v)) and TeO(3+1); Te2O7(6-) (bridged tetrahedral), we have carried out ab initio frequency calculations for tpy TeO3(2-) (triagonal pyramidal, C(3v) and C(s)) and tp TeO3(2-) (triagonal planar, D(3h)) ions. The quantum mechanical calculations at the levels of RHF, B3LYP and MP2 allow confident vibrational assignments and structural identification in the binary oxide glass (95% alpha-TeO2 +5% Sm2O3). The dominant three-dimensional network structures in the modified glass are triagonal pyramidal TeO3 with minor features of short range distorted tbp TeO4 and bridged tetrahedral unit of TeO(3+1), leading to a structure of infinite chain. Therefore, alpha-TeO2/Sm2O3 (95/5%) glass experience structural changes from TeO4 (tbp); Te2O7 (TeO(3+1))-->TeO3 (tpy).
Shaltout, I.; Mohamed, Tarek A.
2007-06-01
Chozen system of tellurite glasses doped with rare earth oxides (95% α-TeO 2 + 5% Sm 2O 3) was prepared by melt quenching. Consequently, the Raman spectrum (150-1250 cm -1) of the modified tellurite have been recorded. As a continuation to our normal coordinate analysis, force constants and quantum mechanical (QM) calculations for tbp TeO 44- (triagonal bipyramid, C2v) and TeO 3+1; Te 2O 76- (bridged tetrahedral), we have carried out ab initio frequency calculations for tpy TeO 32- (triagonal pyramidal, C3v and Cs) and tp TeO 32- (triagonal planar, D3h) ions. The quantum mechanical calculations at the levels of RHF, B3LYP and MP2 allow confident vibrational assignments and structural identification in the binary oxide glass (95% α-TeO 2 + 5% Sm 2O 3). The dominant three-dimensional network structures in the modified glass are triagonal pyramidal TeO 3 with minor features of short range distorted tbp TeO 4 and bridged tetrahedral unit of TeO 3+1, leading to a structure of infinite chain. Therefore, α-TeO 2/Sm 2O 3 (95/5%) glass experience structural changes from TeO 4 (tbp); Te 2O 7 (TeO 3+1) → TeO 3 (tpy).
Dolev, S; Kolenda, N
2005-01-01
For more than a century, quantum mechanics has served as a very powerful theory that has expanded physics and technology far beyond their classical limits, yet it has also produced some of the most difficult paradoxes known to the human mind. This book represents the combined efforts of sixteen of today's most eminent theoretical physicists to lay out future directions for quantum physics. The authors include Yakir Aharonov, Anton Zeilinger; the Nobel laureates Anthony Leggett and Geradus 't Hooft; Basil Hiley, Lee Smolin and Henry Stapp. Following a foreword by Roger Penrose, the individual chapters address questions such as quantum non-locality, the measurement problem, quantum insights into relativity, cosmology and thermodynamics, and the possible bearing of quantum phenomena on biology and consciousness.
Mayato, R; Egusquiza, I
2002-01-01
The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the theory. This book describes the problems, and the attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory, such as the parametric (clock) time, tunneling times, decay times, dwell times, delay times, arrival times or jump times. This multiauthored book, written as an introductory guide for the non-initiated as well as a useful source of information for the expert, covers many of the open questions. A brief historical overview is to be found in the introduction. It is followed by 12 chapters devoted to conceptual and theoretical investigations as well as experimental issues in quantum-mechanical time measurements. This unique monograph should attract physicists as well as philosophers of science working in the foundations of quantum physics.
Probability in quantum mechanics
Directory of Open Access Journals (Sweden)
J. G. Gilson
1982-01-01
Full Text Available By using a fluid theory which is an alternative to quantum theory but from which the latter can be deduced exactly, the long-standing problem of how quantum mechanics is related to stochastic processes is studied. It can be seen how the Schrödinger probability density has a relationship to time spent on small sections of an orbit, just as the probability density has in some classical contexts.
Mechanics classical and quantum
Taylor, T T
2015-01-01
Mechanics: Classical and Quantum explains the principles of quantum mechanics via the medium of analytical mechanics. The book describes Schrodinger's formulation, the Hamilton-Jacobi equation, and the Lagrangian formulation. The author discusses the Harmonic Oscillator, the generalized coordinates, velocities, as well as the application of the Lagrangian formulation to systems that are partially or entirely electromagnetic in character under certain conditions. The book examines waves on a string under tension, the isothermal cavity radiation, and the Rayleigh-Jeans result pertaining to the e
Thermodynamic integration from classical to quantum mechanics.
Habershon, Scott; Manolopoulos, David E
2011-12-14
We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.
The quantum mechanics of cosmology.
Hartle, James B.
The following sections are included: * INTRODUCTION * POST-EVERETT QUANTUM MECHANICS * Probability * Probabilities in general * Probabilities in Quantum Mechanics * Decoherent Histories * Fine and Coarse Grained Histories * Decohering Sets of Coarse Grained Histories * No Moment by Moment Definition of Decoherence * Prediction, Retrodiction, and History * Prediction and Retrodiction * The Reconstruction of History * Branches (Illustrated by a Pure ρ) * Sets of Histories with the Same Probabilities * The Origins of Decoherence in Our Universe * On What Does Decoherence Depend? * Two Slit Model * The Caldeira-Leggett Oscillator Model * The Evolution of Reduced Density Matrices * Towards a Classical Domain * The Branch Dependence of Decoherence * Measurement * The Ideal Measurement Model and the Copenhagen Approximation to Quantum Mechanics * Approximate Probabilities Again * Complex Adaptive Systems * Open Questions * GENERALIZED QUANTUM MECHANICS * General Features * Hamiltonian Quantum Mechanics * Sum-Over-Histories Quantum Mechanics for Theories with a Time * Differences and Equivalences between Hamiltonian and Sum-Over-Histories Quantum Mechanics for Theories with a Time * Classical Physics and the Classical Limit of Quantum Mechanics * Generalizations of Hamiltonian Quantum Mechanics * TIME IN QUANTUM MECHANICS * Observables on Spacetime Regions * The Arrow of Time in Quantum Mechanics * Topology in Time * The Generality of Sum Over Histories Quantum Mechanics * THE QUANTUM MECHANICS OF SPACETIME * The Problem of Time * General Covariance and Time in Hamiltonian Quantum Mechanics * The "Marvelous Moment" * A Quantum Mechanics for Spacetime * What we Need * Sum-Over-Histories Quantum Mechanics for Theories Without a Time * Sum-Over-Spacetime-Histories Quantum Mechanics * Extensions and Contractions * The Construction of Sums Over Spacetime Histories * Some Open Questions * PRACTICAL QUANTUM COSMOLOGY * The Semiclassical Regime * The Semiclassical Approximation
Directory of Open Access Journals (Sweden)
Iqmal Tahir
2010-06-01
Full Text Available Modeling of several alkyl salicylates based on electronic transition by using semiempriical mechanical quantum ZINDO/s calculation has been done. Object of these research were assumed only alkyl salicylates of C4 (butyl until C8 (octyl homologue with 4-7 example structures of each homologue. All of the computation have been performed using quantum chemistry - package software Hyperchem 6.0. The research covered about drawing each of the structure, geometry optimization using semiempirical AM1 algorithm and followed with single point calculation using semiempirical ZINDO/s technique. ZINDO/s calculations used a defined criteria that is singly excited - Configuration Interaction (CI, gap of HOMO-LUMO energy transition was 2 and degeneracy level was 3. Analysis of the theoretical spectra was focused in the UV-B (290-320 nm and UV-C (200-290 nm area. The result showed that modeling of the compound can be used for predicting the type of UV protection activity depending with the electronic transition in the UV area. Modification of the alkyl homologue relatively did not change the value of wavelength absorbtion to indicate the UV protection activity. Alkyl salicylate compounds were predicted as UV-C sunscreen or relatively the compounds have protection effect for UV-C. Keywords: alkyl salicylate, sunscreen, semiempirical methods
Non-relativistic quantum mechanics
Puri, Ravinder R.
2017-01-01
This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...
Li, Ming-Juan; Liu, Ming-Xia; Zhao, Yan-Ying; Pei, Ke-Mei; Wang, Hui-Gang; Zheng, Xuming; Fang, Wei Hai
2013-10-03
The resonance Raman spectroscopic study of the excited state structural dynamics of 1,3-dimethyluracil (DMU), 5-bromo-1,3-dimethyluracil (5BrDMU), uracil, and thymine in water and acetonitrile were reported. Density functional theory calculations were carried out to help elucidate the ultraviolet electronic transitions associated with the A-, and B-band absorptions and the vibrational assignments of the resonance Raman spectra. The effect of the methylation at N1, N3 and C5 sites of pyrimidine ring on the structural dynamics of uracils in different solvents were explored on the basis of the resonance Raman intensity patterns. The relative resonance Raman intensities of DMU and 5BrDMU are computed at the B3LYP-TD level. Huge discrepancies between the experimental resonance Raman intensities and the B3LYP-TD predicted ones were observed. The underlying mechanism was briefly discussed. The decay channel through the S1((1)nπ*)/S2((1)ππ*) conical intersection and the S1((1)nπ*)/T1((3)ππ*) intersystem crossing were revealed by using the CASSCF(8,7)/6-31G(d) level of theory calculations.
Fundamentals of quantum mechanics
House, J E
2017-01-01
Fundamentals of Quantum Mechanics, Third Edition is a clear and detailed introduction to quantum mechanics and its applications in chemistry and physics. All required math is clearly explained, including intermediate steps in derivations, and concise review of the math is included in the text at appropriate points. Most of the elementary quantum mechanical models-including particles in boxes, rigid rotor, harmonic oscillator, barrier penetration, hydrogen atom-are clearly and completely presented. Applications of these models to selected “real world” topics are also included. This new edition includes many new topics such as band theory and heat capacity of solids, spectroscopy of molecules and complexes (including applications to ligand field theory), and small molecules of astrophysical interest.
Quantum Mechanics with Applications
Afnan, Iraj R
2011-01-01
The ebook introduces undergraduate students to the basic skills required to use non-relativistic quantum mechanics for bound and scattering problems in atomic, molecular and nuclear physics. Initial emphasis is on problems that admit analytic solutions. These results are then used in conjunction with symmetry to develop approximation methods for both bound and scattering problems. The text concentrates on the application of computational problems to introduce the basic concepts of quantum mechanics. These are then used to study more complex problems that can be reduced to one-body problems.
Kogan, VI; Gersch, Harold
2011-01-01
Written by a pair of distinguished Soviet mathematicians, this compilation presents 160 lucidly expressed problems in nonrelativistic quantum mechanics plus completely worked-out solutions. Some were drawn from the authors' courses at the Moscow Institute of Engineering, but most were prepared especially for this book. A high-level supplement rather than a primary text, it constitutes a masterful complement to advanced undergraduate and graduate texts and courses in quantum mechanics.The mathematics employed in the proofs of the problems-asymptotic expansions of functions, Green's functions, u
Saxon, David S
2012-01-01
Based on lectures for an undergraduate UCLA course in quantum mechanics, this volume focuses on the formulas of quantum mechanics rather than applications. Widely used in both upper-level undergraduate and graduate courses, it offers a broad self-contained survey rather than in-depth treatments.Topics include the dual nature of matter and radiation, state functions and their interpretation, linear momentum, the motion of a free particle, Schrödinger's equation, approximation methods, angular momentum, and many other subjects. In the interests of keeping the mathematics as simple as possible, m
Noncommutative quantum mechanics
Gamboa, J.; Loewe, M.; Rojas, J. C.
2001-09-01
A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.
Hollowood, Timothy J.
2016-07-01
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists' laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr's quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.
Time Asymmetric Quantum Mechanics
Directory of Open Access Journals (Sweden)
Arno R. Bohm
2011-09-01
Full Text Available The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1 for states or the Heisenberg equation (6a for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus and observables (defined by a registration apparatus (detector. If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t_0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.
Quantum biological channel modeling and capacity calculation.
Djordjevic, Ivan B
2012-12-10
Quantum mechanics has an important role in photosynthesis, magnetoreception, and evolution. There were many attempts in an effort to explain the structure of genetic code and transfer of information from DNA to protein by using the concepts of quantum mechanics. The existing biological quantum channel models are not sufficiently general to incorporate all relevant contributions responsible for imperfect protein synthesis. Moreover, the problem of determination of quantum biological channel capacity is still an open problem. To solve these problems, we construct the operator-sum representation of biological channel based on codon basekets (basis vectors), and determine the quantum channel model suitable for study of the quantum biological channel capacity and beyond. The transcription process, DNA point mutations, insertions, deletions, and translation are interpreted as the quantum noise processes. The various types of quantum errors are classified into several broad categories: (i) storage errors that occur in DNA itself as it represents an imperfect storage of genetic information, (ii) replication errors introduced during DNA replication process, (iii) transcription errors introduced during DNA to mRNA transcription, and (iv) translation errors introduced during the translation process. By using this model, we determine the biological quantum channel capacity and compare it against corresponding classical biological channel capacity. We demonstrate that the quantum biological channel capacity is higher than the classical one, for a coherent quantum channel model, suggesting that quantum effects have an important role in biological systems. The proposed model is of crucial importance towards future study of quantum DNA error correction, developing quantum mechanical model of aging, developing the quantum mechanical models for tumors/cancer, and study of intracellular dynamics in general.
Quantum Biological Channel Modeling and Capacity Calculation
Directory of Open Access Journals (Sweden)
Ivan B. Djordjevic
2012-12-01
Full Text Available Quantum mechanics has an important role in photosynthesis, magnetoreception, and evolution. There were many attempts in an effort to explain the structure of genetic code and transfer of information from DNA to protein by using the concepts of quantum mechanics. The existing biological quantum channel models are not sufficiently general to incorporate all relevant contributions responsible for imperfect protein synthesis. Moreover, the problem of determination of quantum biological channel capacity is still an open problem. To solve these problems, we construct the operator-sum representation of biological channel based on codon basekets (basis vectors, and determine the quantum channel model suitable for study of the quantum biological channel capacity and beyond. The transcription process, DNA point mutations, insertions, deletions, and translation are interpreted as the quantum noise processes. The various types of quantum errors are classified into several broad categories: (i storage errors that occur in DNA itself as it represents an imperfect storage of genetic information, (ii replication errors introduced during DNA replication process, (iii transcription errors introduced during DNA to mRNA transcription, and (iv translation errors introduced during the translation process. By using this model, we determine the biological quantum channel capacity and compare it against corresponding classical biological channel capacity. We demonstrate that the quantum biological channel capacity is higher than the classical one, for a coherent quantum channel model, suggesting that quantum effects have an important role in biological systems. The proposed model is of crucial importance towards future study of quantum DNA error correction, developing quantum mechanical model of aging, developing the quantum mechanical models for tumors/cancer, and study of intracellular dynamics in general.
Determinism beneath Quantum Mechanics
Hooft, G
2002-01-01
Contrary to common belief, it is not difficult to construct deterministic models where stochastic behavior is correctly described by quantum mechanical amplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What is difficult however is to obtain a Hamiltonian that is bounded from below, and whose ground state is a vacuum that exhibits complicated vacuum fluctuations, as in the real world. Beneath Quantum Mechanics, there may be a deterministic theory with (local) information loss. This may lead to a sufficiently complex vacuum state, and to an apparent non-locality in the relation between the deterministic ("ontological") states and the quantum states, of the kind needed to explain away the Bell inequalities. Theories of this kind would not only be appealing from a philosophical point of view, but may also be essential for understanding causality at Planckian distance scales.
Relativistic quantum mechanics
Wachter, Armin
2010-01-01
Which problems do arise within relativistic enhancements of the Schrödinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way. The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the...
Institute of Scientific and Technical Information of China (English)
吴宁; 阮图南
1996-01-01
A quantum mechanical model with one bosonic degree of freedom is discussed in detail. Conventionally, when a quantum mechanical model is constructed, one must know the corresponding classical model. And by applying the correspondence between the classical Poisson brackets and the canonical commutator, the canonical quantization condition can be obtained. In the quantum model, study of the corresponding classical model is needed first. In this model, the Lagrangian is an operator gauge invariant. After localization, in order to keep gauge invariance, the operator gauge potential must be introduced. The Eular-Lagrange equation of motion of the dynamical argument gives the usual operator equation of motion. And the operator gauge potential just gjves a constraint. This constraint is just the usual canonical quantization condition.
Quantum Tunneling In Deformed Quantum Mechanics with Minimal Length
Guo, Xiaobo; Tao, Jun; Wang, Peng
2016-01-01
In the deformed quantum mechanics with a minimal length, one WKB connection formula through a turning point is derived. We then use it to calculate tunnelling rates through potential barriers under the WKB approximation. Finally, the minimal length effects on two examples of quantum tunneling in nuclear and atomic physics are discussed
Mullin, Jonathan; Schatz, George C
2012-03-01
A multiscale method is presented that allows for evaluation of plasmon-enhanced optical properties of nanoparticle/molecule complexes with no additional cost compared to standard electrodynamics (ED) and linear response quantum mechanics (QM) calculations for the particle and molecule, respectively, but with polarization and orientation effects automatically described. The approach first calculates the total field of the nanoparticle by ED using the finite difference time domain (FDTD) method. The field intensity in the frequency domain as a function of distance from the nanoparticle is calculated via a Fourier transform. The molecular optical properties are then calculated with QM in the frequency domain in the presence of the total field of the nanoparticle. Back-coupling due to dipolar reradiation effects is included in the single-molecule plane wave approximation. The effects of polarization and partial orientation averaging are considered. The QM/ED method is evaluated for the well-characterized test case of surface-enhanced Raman scattering (SERS) of pyridine bound to silver, as well as for the resonant Raman chromophore rhodamine 6G. The electromagnetic contribution to the enhancement factor is 10(4) for pyridine and 10(2) for rhodamine 6G. © 2012 American Chemical Society
Quantum Monte Carlo Calculations of Light Nuclei
Pieper, Steven C
2007-01-01
During the last 15 years, there has been much progress in defining the nuclear Hamiltonian and applying quantum Monte Carlo methods to the calculation of light nuclei. I describe both aspects of this work and some recent results.
Hollowood, Timothy J
2013-01-01
We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one, but does not suffer from the range of problems that plague other modal interpretations. The key feature is that quantum states carry an additional property assignment in the form of one the eigenvectors of the reduced density matrix which evolves evolves according to a stochastic process driven by the unmodified Schrodinger equation, but it is usually hidden from the emergent classical description due to the ergodic nature of its dynamics. However, during a quantum measurement, ergodicity is broken by decoherence and definite outcomes occur with probabilities that agree with the Born rule.
Quantum mechanics with applications
Beard, David B
2014-01-01
This introductory text emphasizes Feynman's development of path integrals and its application to wave theory for particles. Suitable for undergraduate and graduate students of physics, the well-written, clear, and rigorous text was written by two of the nation's leading authorities on quantum physics. A solid foundation in quantum mechanics and atomic physics is assumed. Early chapters provide background in the mathematical treatment and particular properties of ordinary wave motion that also apply to particle motion. The close relation of quantum theory to physical optics is stressed. Subsequent sections emphasize the physical consequences of a wave theory of material properties, and they offer extensive applications in atomic physics, nuclear physics, solid state physics, and diatomic molecules. Four helpful Appendixes supplement the text.
Epigenetics: Biology's Quantum Mechanics.
Jorgensen, Richard A
2011-01-01
The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920s and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider.
Epigenetics: Biology's Quantum Mechanics
Directory of Open Access Journals (Sweden)
Richard A Jorgensen
2011-04-01
Full Text Available The perspective presented here is that modern genetics is at a similar stage of development as were early formulations of quantum mechanics theory in the 1920's and that in 2010 we are at the dawn of a new revolution in genetics that promises to enrich and deepen our understanding of the gene and the genome. The interrelationships and interdependence of two views of the gene - the molecular biological view and the epigenetic view - are explored, and it is argued that the classical molecular biological view is incomplete without incorporation of the epigenetic perspective and that in a sense the molecular biological view has been evolving to include the epigenetic view. Intriguingly, this evolution of the molecular view toward the broader and more inclusive epigenetic view of the gene has an intriguing, if not precise, parallel in the evolution of concepts of atomic physics from Newtonian mechanics to quantum mechanics that are interesting to consider.
Shiga, Motoyuki; Tachikawa, Masanori; Miura, Shinichi
2000-12-01
We present an accurate calculational scheme for many-body systems composed of electrons and nuclei, by path integral molecular dynamics technique combined with the ab initio molecular orbital theory. Based upon the scheme, the simulation of a water molecule at room temperature is demonstrated, applying all-electron calculation at the Hartree-Fock level of theory.
Advanced concepts in quantum mechanics
Esposito, Giampiero; Miele, Gennaro; Sudarshan, George
2015-01-01
Introducing a geometric view of fundamental physics, starting from quantum mechanics and its experimental foundations, this book is ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. Focusing on structural issues and geometric ideas, this book guides readers from the concepts of classical mechanics to those of quantum mechanics. The book features an original presentation of classical mechanics, with the choice of topics motivated by the subsequent development of quantum mechanics, especially wave equations, Poisson brackets and harmonic oscillators. It also presents new treatments of waves and particles and the symmetries in quantum mechanics, as well as extensive coverage of the experimental foundations.
Zhang, Y. C.; Zhang, J. Z. H.; Kouri, D. J.; Haug, K.; Schwenke, D. W.
1988-01-01
Numerically exact, fully three-dimensional quantum mechanicl reactive scattering calculations are reported for the H2Br system. Both the exchange (H + H-prime Br to H-prime + HBr) and abstraction (H + HBR to H2 + Br) reaction channels are included in the calculations. The present results are the first completely converged three-dimensional quantum calculations for a system involving a highly exoergic reaction channel (the abstraction process). It is found that the production of vibrationally hot H2 in the abstraction reaction, and hence the extent of population inversion in the products, is a sensitive function of initial HBr rotational state and collision energy.
Symmetry and quantum mechanics
Corry, Scott
2016-01-01
This book offers an introduction to quantum mechanics for professionals, students, and others in the field of mathematics who have a minimal background in physics with an understanding of linear algebra and group theory. It covers such topics as Lie groups, algebras and their representations, and analysis (Hilbert space, distributions, the spectral Theorem, and the Stone-Von Neumann Theorem). The book emphasizes the role of symmetry and is useful to physicists as it provides a mathematical introduction to the topic.
Graduate Quantum Mechanics Reform
Carr, L D
2008-01-01
We address four main areas in which graduate quantum mechanics education in the U.S. can be improved: course content; textbook; teaching methods; and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all four of these areas. In particular, we have modified the content of the course to reflect progress in the field in the last 50 years, use modern textbooks that include such content, incorporate a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We present a new assessment tool, the Graduate Quantum Mechanics Conceptual Survey, and further testing of a previously developed assessment tool, the Quantum Mechanics Conceptual Survey (QMCS). We find that graduate students respond well to research-based techniques that have previously been tested mainly in introductory courses, and that they learn a great deal of the new content introduced in each ve...
Quantum Mechanics in the Infrared
Radicevic, Djordje
2016-01-01
This paper presents an algebraic formulation of the renormalization group flow in quantum mechanics on flat target spaces. For any interacting quantum mechanical theory, the fixed point of this flow is a theory of classical probability, not a different effective quantum mechanics. Each energy eigenstate of the UV Hamiltonian flows to a probability distribution whose entropy is a natural diagnostic of quantum ergodicity of the original state. These conclusions are supported by various examples worked out in detail.
Energy Technology Data Exchange (ETDEWEB)
Pirojsirikul, Teerapong [Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive La Jolla California 92093; Götz, Andreas W. [San Diego Supercomputer Center, University of California San Diego, 9500 Gilman Drive La Jolla California 92093; Weare, John [Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive La Jolla California 92093; Walker, Ross C. [Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive La Jolla California 92093; GlaxoSmithKline, 1250 S. Collegeville Road Collegeville Pennsylvania 19426; Kowalski, Karol [Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P. O. Box 999 Richland Washington 99352; Valiev, Marat [Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P. O. Box 999 Richland Washington 99352
2017-05-03
Green Fluorescent Protein (GFP) is a widely used fluorescent biomarker for the study of biological systems. Our investigation is focused on providing a reliable theoretical description of the GFP chromophore, the photochemical properties of which can be influenced through both the surrounding protein environment and pH levels. In this work we are specifically addressing the effect of an aqueous solvation environment , where a number of experimental measurements have been performed. Our approach is based on a combined quantum mechanics molecular mechanics (QM/MM) methodology, which incorporates high level coupled cluster theory for the analysis of excited states. It also presents the first application of the newly developed NWChem/AMBER QM/MM interface. Using a systematic approach, which involves comparison of gas phase and aqueous results for different protonation states and conformations, we have resolved existing uncertainties regarding theoretical interpretation of the experimental data. We observe that the impact of aqueous environment on charged states generally results in blue shifts, but the magnitude of the effect is sensitive to charge state and conformation and can be rationalized based on charge movement into the area of higher/lower external electrostatic potentials. At neutral pH levels the experimentally observed absorption signal is most likely coming from the phenol protonated form. Our results also show that the high level coupled description is essential for proper description of excited states of GFP.
Jensen, Jan H
2013-01-01
A new web-server called The Molecule Calculator (MolCalc) is presented. The entry page is a molecular editor (JSmol) for interactive molecule building. The resulting structure can then be used to estimate molecular properties such as heats of formation and other thermodynamic properties, vibrational frequencies and vibrational modes, and molecular orbitals and orbital energies. These properties are computed using the GAMESS program at either the RHF/STO-3G (orbitals and orbital energies) or PM3 level of theory (all other properties) in a matter of seconds or minutes depending on the size of the molecule. The results, though approximate, can help students develop a "chemical intuition" about how molecular structure affects molecular properties, without performing the underlying calculations by hand, a near impossible task for all but the simplest chemical systems.
Basdevant, Jean-Louis
2007-01-01
Beautifully illustrated and engagingly written, Lectures on Quantum Mechanics presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevant's style is clear and stimulating, in the manner of a brisk classroom lecture that students can follow with ease and enjoyment. Here is a sample of the book's style, from the opening of Chapter 1: "If one were to ask a passer-by to quote a great formula of physics, chances are that the answer would be 'E = mc2'. Nevertheless, the formula 'E=hV' which was written in the same year 1905 by the same Albert Einstein, and which started quantum theory, concerns their daily life considerably more. In fact, of the three watershed years for physics toward the beginning of the 20th century - 1905: the Special Relativity of Einstein, Lorentz and Poincaré; 1915: the General Relativity of Einstein, with its extraordinary reflections on gravitation, space and time; and 1925: the full development of Quantum Mechanics - it is surely the last which has the mos...
Hollowood, Timothy J
2015-01-01
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950's development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrodinger cat states are the norm rather than curiosities generat...
Quantum mechanics II a second course in quantum theory
Landau, Rubin H
2004-01-01
Here is a readable and intuitive quantum mechanics text that covers scattering theory, relativistic quantum mechanics, and field theory. This expanded and updated Second Edition - with five new chapters - emphasizes the concrete and calculable over the abstract and pure, and helps turn students into researchers without diminishing their sense of wonder at physics and nature.As a one-year graduate-level course, Quantum Mechanics II: A Second Course in Quantum Theory leads from quantum basics to basic field theory, and lays the foundation for research-oriented specialty courses. Used selectively, the material can be tailored to create a one-semester course in advanced topics. In either case, it addresses a broad audience of students in the physical sciences, as well as independent readers - whether advanced undergraduates or practicing scientists
Sakurai, Jun John
2011-01-01
This best-selling classic provides a graduate-level, non-historical, modern introduction of quantum mechanical concepts. The author, J. J. Sakurai, was a renowned theorist in particle theory. This revision by Jim Napolitano retains the original material and adds topics that extend the text’s usefulness into the 21st century. The introduction of new material, and modification of existing material, appears in a way that better prepares the student for the next course in quantum field theory. You will still find such classic developments as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell’s inequality. The style and treatment of topics is now more consistent across chapters.
Bananaworld quantum mechanics for primates
Bub, Jeffrey
2016-01-01
What on earth do bananas have to do with quantum mechanics? From a modern perspective, quantum mechanics is about strangely counterintuitive correlations between separated systems, which can be exploited in feats like quantum teleportation, unbreakable cryptographic schemes, and computers with enormously enhanced computing power. Schro?dinger coined the term "entanglement" to describe these bizarre correlations. Bananaworld -- an imaginary island with "entangled" bananas -- brings to life the fascinating discoveries of the new field of quantum information without the mathematical machinery of quantum mechanics. The connection with quantum correlations is fully explained in sections written for the non-physicist reader with a serious interest in understanding the mysteries of the quantum world. The result is a subversive but entertaining book that is accessible and interesting to a wide range of readers, with the novel thesis that quantum mechanics is about the structure of information. What we have discovered...
Quantum mechanics theory and experiment
Beck, Mark
2012-01-01
This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...
Scan Quantum Mechanics: Quantum Inertia Stops Superposition
Gato-Rivera, Beatriz
2015-01-01
A novel interpretation of the quantum mechanical superposition is put forward. Quantum systems scan all possible available states and switch randomly and very rapidly among them. The longer they remain in a given state, the larger the probability of the system to be found in that state during a measurement. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia $I_q$ reaches a critical value $I_{cr}$ for an observable, the switching among the different eigenvalues of that observable stops and the corresponding superposition comes to an end. Consequently, increasing the mass, temperature, gravitational force, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. The process could be reversible decreasing the size, temperature, gravitational force, etc. leading to...
Murakami, Mitsuko; Kirchner, Tom; Horbatsch, Marko; Lüdde, Hans Jürgen
2012-08-01
Electron removal and fragmentation cross sections are calculated for He+(1s)-H2O collisions at impact energies from 20 keV/amu to several MeV/amu by using the nonperturbative basis generator method for ion-molecule collisions. Previous work for proton impact is extended to deal with the dressed projectile in the present case. The effects from the active projectile electron are taken into account by applying the same single-particle Hamiltonian to all electrons and by using the inclusive-probability formalism in the final-state analysis. Fragment-ion yields are evaluated from the single-, double-, and triple-electron removal cross sections, and the results are compared with the available experimental data. Very reasonable agreement is obtained for fragmentation caused by direct ionization, while some discrepancies remain in the capture and loss data.
Energy Technology Data Exchange (ETDEWEB)
Dong Cunku [Department of Chemistry, Harbin Institute of Technology, Harbin 150090 (China); Li Xin, E-mail: lixin@hit.edu.cn [Department of Chemistry, Harbin Institute of Technology, Harbin 150090 (China); Guo Zechong [School of Municipal Environmental Engineering, Harbin Institute of Technology, Harbin 150090 (China); Qi Jingyao, E-mail: jyq@hit.edu.cn [School of Municipal Environmental Engineering, Harbin Institute of Technology, Harbin 150090 (China)
2009-08-04
A new rational approach for the preparation of molecularly imprinted polymer (MIP) based on the combination of molecular dynamics (MD) simulations and quantum mechanics (QM) calculations is described in this work. Before performing molecular modeling, a virtual library of functional monomers was created containing forty frequently used monomers. The MD simulations were first conducted to screen the top three monomers from virtual library in each porogen-acetonitrile, chloroform and carbon tetrachloride. QM simulations were then performed with an aim to select the optimum monomer and progen solvent in which the QM simulations were carried out; the monomers giving the highest binding energies were chosen as the candidate to prepare MIP in its corresponding solvent. The acetochlor, a widely used herbicide, was chosen as the target analyte. According to the theoretical calculation results, the MIP with acetochlor as template was prepared by emulsion polymerization method using N,N-methylene bisacrylamide (MBAAM) as functional monomer and divinylbenzene (DVB) as cross-linker in chloroform. The synthesized MIP was then tested by equilibrium-adsorption method, and the MIP demonstrated high removal efficiency to the acetochlor. Mulliken charge distribution and {sup 1}H NMR spectroscopy of the synthesized MIP provided insight on the nature of recognition during the imprinting process probing the governing interactions for selective binding site formation at a molecular level. We think the computer simulation method first proposed in this paper is a novel and reliable method for the design and synthesis of MIP.
Dubnikova, Faina; Tamburu, Carmen; Lifshitz, Assa
2016-09-29
The isomerization of o-quinolyl ↔ o-isoquinolyl radicals and their thermal decomposition were studied by quantum chemical methods, where potential energy surfaces of the reaction channels and their kinetics rate parameters were determined. A detailed kinetics scheme containing 40 elementary steps was constructed. Computer simulations were carried out to determine the isomerization mechanism and the distribution of reaction products in the decomposition. The calculated mole percent of the stable products was compared to the experimental values that were obtained in this laboratory in the past, using the single pulse shock tube. The agreement between the experimental and the calculated mole percents was very good. A map of the figures containing the mole percent's of eight stable products of the decomposition plotted vs T are presented. The fast isomerization of o-quinolyl → o-isoquinolyl radicals via the intermediate indene imine radical and the attainment of fast equilibrium between these two radicals is the reason for the identical product distribution regardless whether the reactant radical is o-quinolyl or o-isoquinolyl. Three of the main decomposition products of o-quinolyl radical, are those containing the benzene ring, namely, phenyl, benzonitrile, and phenylacetylene radicals. They undergo further decomposition mainly at high temperatures via two types of reactions: (1) Opening of the benzene ring in the radicals, followed by splitting into fragments. (2) Dissociative attachment of benzonitrile and phenyl acetylene by hydrogen atoms to form hydrogen cyanide and acetylene.
Quantum mechanics of leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Mendizabal Cofre, Sebastian
2010-08-15
Leptogenesis is an attractive mechanism that simultaneously explains the matterantimatter asymmetry of the universe as well as the small masses of the standard model neutrinos. This is performed by naturally extending the standard model with the insertion of right handed neutrinos. Leptogenesis is usually studied via the semi-classical Boltzmann equations. However, these equations suffer from basic conceptual problems and they lack to include many quantum phenomena, such as memory effects and coherence oscillations. In order to fully describe leptogenesis, a full quantum treatment is required. In this work we show how to address leptogenesis systematically in a purely quantum way. We start by studying scalar and fermionic excitations in a plasma by solving the Kadanoff-Baym equations of motion for Green's functions, with significant emphasis on the initial and boundary conditions of the solutions. We compute analytically the asymmetry generated from the departure of equilibrium of a particle in a thermal bath. The comparison with the semi-classical Boltzmann approach is also analysed, leading to a qualitative difference between both methods. The non-locality of the Kadanoff-Baym equations shows how off-shell effects can have a huge impact on the generated asymmetry, effects that cannot be studied with the Boltzmann equations. The insertion of standard model interactions like the decay widths for the particles of the bath is also discussed. We explain how with a trivial insertion of these widths we regain locality on the processes, i.e. we regain the Boltzmann equations. (orig.)
Exactly Solvable Quantum Mechanics
Sasaki, Ryu
2014-01-01
A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main subjects to be discussed are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modifications), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, coherent states, various deformation schemes (multiple Darboux transformations) and the infinite families of multi-indexed orthogonal polynomials, the exceptional orthogonal polynomials, and deformed exactly solvable scattering problems.
Shaaban, Ibrahim A.; Karoyo, Abdalla; Wilson, Lee D.; Mohamed, Tarek A.
2017-08-01
The Raman spectrum (3700-100 cm- 1) of meso-2,3-Dimercaptosuccinic acid (meso-DMSA; C4H6O4S2) was recorded in the solid phase using 514.5 and 785 nm excitation lines. Whereas, the DRIFT spectrum (4000-400 cm- 1) of the sample powdered in KBr was obtained. Moreover, DFT-B3LYP/6-31G(d) geometry optimization and frequency calculations were carried out for centrosymmetric trans (Ci), gauche (C1; G+/G-) and eclipsed (Cs; Ef and C1; E+/E-) rotational isomers in favor of a trans conformation, the least energy with real frequencies. However, other conformers were found at either local minima or local maxima as a result of the rotation of carboxyl, hydroxyl and thiol groups according to a potential energy surface scan. Moreover, an imaginary wavenumber was predicted; therefore, they are considered transition states. On the other hand, the mass spectrum of the sample dissolved in an acetonitrile/methanol mixture reveal 4-6% dimer through intermolecular hydrogen bonding interactions via the dicarboxylic groups. Therefore, we have modeled the complex structure obeying Ci restricted symmetry for an isolated dimer unit using DFT-B3LYP/6-31G(d) and for two molecules per unit cell in the solid phase implementing DFT-PBE functional. Thus, the meso-DMSA forms long strands in which individual molecules are bonded together at each termini through hydrogen bonding. Aided by normal coordinate analysis, complete vibrational assignments were provided herein which support Ci configuration of meso-DMSA in the solid state which found consistent with the observed broadening, composite, split bands, and the mutual exclusion rule.
The quantum mechanics of materials
Cohen, M. L.; Heine, V.; Phillips, J. C.
1982-06-01
The prediction of the properties of materials from fundamental principles, i.e., quantum mechanics, by the use of pseudopotential theory is discussed. Following a review of previous difficulties encountered in the application of quantum theory to complex aggregates of matter, and the failures of early theories to resolve differences corresponding to important phase transitions in solids, the idea first proposed by Herring concerning the energy cancellation of valence electrons and the possibility of neglecting core electron effects is examined as the basis of pseudopotential theory. The application of the electron pseudopotential, representing the scattering strength of one atomic core with respect to a single Fourier component of one valence-electron wave, to the calculation of the scattering of an electron wave in crystalline solids is examined, and the derivation of structural properties from the pseudopotentials is discussed. Recent advances in pseudopotential theory explaining the properties of surface and interface structures, and the total energy of semiconducting materials are indicated.
Relaxation Method For Calculating Quantum Entanglement
Tucci, R R
2001-01-01
In a previous paper, we showed how entanglement of formation can be defined as a minimum of the quantum conditional mutual information (a.k.a. quantum conditional information transmission). In classical information theory, the Arimoto-Blahut method is one of the preferred methods for calculating extrema of mutual information. We present a new method akin to the Arimoto-Blahut method for calculating entanglement of formation. We also present several examples computed with a computer program called Causa Comun that implements the ideas of this paper.
Quantum Mechanics and Quantum Field Theory
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
Quantum mechanical streamlines. I - Square potential barrier
Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.
1974-01-01
Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.
Submicroscopic Deterministic Quantum Mechanics
Krasnoholovets, V
2002-01-01
So-called hidden variables introduced in quantum mechanics by de Broglie and Bohm have changed their initial enigmatic meanings and acquired quite reasonable outlines of real and measurable characteristics. The start viewpoint was the following: All the phenomena, which we observe in the quantum world, should reflect structural properties of the real space. Thus the scale 10^{-28} cm at which three fundamental interactions (electromagnetic, weak, and strong) intersect has been treated as the size of a building block of the space. The appearance of a massive particle is associated with a local deformation of the cellular space, i.e. deformation of a cell. The mechanics of a moving particle that has been constructed is deterministic by its nature and shows that the particle interacts with cells of the space creating elementary excitations called "inertons". The further study has disclosed that inertons are a substructure of the matter waves which are described by the orthodox wave \\psi-function formalism. The c...
Quantum mechanics using Fradkin's representation
Shajesh, K V; Milton, Kimball A.
2005-01-01
Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum mechanics (field theory in one dimension) and apply it to the solution of Schrodinger's equation for the quantum harmonic oscillator.
Gamification of Quantum Mechanics Teaching
Bjælde, Ole Eggers; Sherson, Jacob
2015-01-01
In this small scale study we demonstrate how a gamified teaching setup can be used effectively to support student learning in a quantum mechanics course. The quantum mechanics games were research games, which were played during lectures and the learning was measured with a pretest/posttest method with promising results. The study works as a pilot study to guide the planning of quantum mechanics courses in the future at Aarhus University in Denmark.
Quantum Mechanics for Electrical Engineers
Sullivan, Dennis M
2011-01-01
The main topic of this book is quantum mechanics, as the title indicates. It specifically targets those topics within quantum mechanics that are needed to understand modern semiconductor theory. It begins with the motivation for quantum mechanics and why classical physics fails when dealing with very small particles and small dimensions. Two key features make this book different from others on quantum mechanics, even those usually intended for engineers: First, after a brief introduction, much of the development is through Fourier theory, a topic that is at
A Quantum Space behind Simple Quantum Mechanics
Directory of Open Access Journals (Sweden)
Chuan Sheng Chew
2017-01-01
Full Text Available In physics, experiments ultimately inform us about what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles. This configuration space (as well as phase space can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold and provides a crucial first link for any theoretical model of quantum space-time at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective.
Quantum mechanics the theoretical minimum
Susskind, Leonard
2014-01-01
From the bestselling author of The Theoretical Minimum, an accessible introduction to the math and science of quantum mechanicsQuantum Mechanics is a (second) book for anyone who wants to learn how to think like a physicist. In this follow-up to the bestselling The Theoretical Minimum, physicist Leonard Susskind and data engineer Art Friedman offer a first course in the theory and associated mathematics of the strange world of quantum mechanics. Quantum Mechanics presents Susskind and Friedman’s crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics. An accessible but rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.
Factorization Method in Quantum Mechanics
Dong, Shi-Hai
2007-01-01
This Work introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the Reader’s disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this classic method are the supersymmetric quantum mechanics, shape invariant potentials and group theoretical approaches. It is no exaggeration to say that this method has become the milestone of these approaches. In fact the Author’s driving force has been his desire to provide a comprehensive review volume that includes some new and significant results about the factorization method in quantum mechanics since the literature is inundated with scattered articles in this field, and to pave the Reader’s way into ...
Decoherence in quantum mechanics and quantum cosmology
Hartle, James B.
1992-01-01
A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.
Relativistic quantum mechanics; Mecanique quantique relativiste
Energy Technology Data Exchange (ETDEWEB)
Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.
Efficient method for the calculation of dissipative quantum transport in quantum cascade lasers.
Greck, Peter; Birner, Stefan; Huber, Bernhard; Vogl, Peter
2015-03-09
We present a novel and very efficient method for calculating quantum transport in quantum cascade lasers (QCLs). It follows the nonequilibrium Green's function (NEGF) framework but sidesteps the calculation of lesser self-energies by replacing them by a quasi-equilibrium expression. This method generalizes the phenomenological Büttiker probe model by taking into account individual scattering mechanisms. It is orders of magnitude more efficient than a fully self-consistent NEGF calculation for realistic devices. We apply this method to a new THz QCL design which works up to 250 K - according to our calculations.
Quantum mechanics II advanced topics
Rajasekar, S
2015-01-01
Quantum Mechanics II: Advanced Topics uses more than a decade of research and the authors’ own teaching experience to expound on some of the more advanced topics and current research in quantum mechanics. A follow-up to the authors introductory book Quantum Mechanics I: The Fundamentals, this book begins with a chapter on quantum field theory, and goes on to present basic principles, key features, and applications. It outlines recent quantum technologies and phenomena, and introduces growing topics of interest in quantum mechanics. The authors describe promising applications that include ghost imaging, detection of weak amplitude objects, entangled two-photon microscopy, detection of small displacements, lithography, metrology, and teleportation of optical images. They also present worked-out examples and provide numerous problems at the end of each chapter.
Quantum inertia stops superposition: Scan Quantum Mechanics
Gato-Rivera, Beatriz
2017-08-01
Scan Quantum Mechanics is a novel interpretation of some aspects of quantum mechanics in which the superposition of states is only an approximate effective concept. Quantum systems scan all possible states in the superposition and switch randomly and very rapidly among them. A crucial property that we postulate is quantum inertia, that increases whenever a constituent is added, or the system is perturbed with all kinds of interactions. Once the quantum inertia Iq reaches a critical value Icr for an observable, the switching among its different eigenvalues stops and the corresponding superposition comes to an end, leaving behind a system with a well defined value of that observable. Consequently, increasing the mass, temperature, gravitational strength, etc. of a quantum system increases its quantum inertia until the superposition of states disappears for all the observables and the system transmutes into a classical one. Moreover, the process could be reversible. Entanglement can only occur between quantum systems because an exact synchronization between the switchings of the systems involved must be established in the first place and classical systems do not have any switchings to start with. Future experiments might determine the critical inertia Icr corresponding to different observables, which translates into a critical mass Mcr for fixed environmental conditions as well as critical temperatures, critical electric and magnetic fields, etc. In addition, this proposal implies a new radiation mechanism from astrophysical objects with strong gravitational fields, giving rise to non-thermal synchrotron emission, that could contribute to neutron star formation. Superconductivity, superfluidity, Bose-Einstein condensates, and any other physical phenomena at very low temperatures must be reanalyzed in the light of this interpretation, as well as mesoscopic systems in general.
Bender, Carl M; DeKieviet, Maarten; Klevansky, S P
2013-04-28
PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics.
Popper's test of Quantum Mechanics
Bramon, A
2005-01-01
A test of quantum mechanics proposed by K. Popper and dealing with two-particle entangled states emitted from a fixed source has been criticized by several authors. Some of them claim that the test becomes inconclusive once all the quantum aspects of the source are considered. Moreover, another criticism states that the predictions attributed to quantum mechanics in Popper's analysis are untenable. We reconsider these criticisms and show that, to a large extend, the `falsifiability' potential of the test remains unaffected.
The theoretical foundations of quantum mechanics
Baaquie, Belal E
2013-01-01
The Theoretical Foundations of Quantum Mechanics addresses fundamental issues that are not discussed in most books on quantum mechanics. This book focuses on analyzing the underlying principles of quantum mechanics and explaining the conceptual and theoretical underpinning of quantum mechanics. In particular, the concepts of quantum indeterminacy, quantum measurement and quantum superposition are analyzed to clarify the concepts that are implicit in the formulation of quantum mechanics. The Schrodinger equation is never solved in the book. Rather, the discussion on the fundamentals of quantum mechanics is treated in a rigorous manner based on the mathematics of quantum mechanics. The new concept of the interplay of empirical and trans-empirical constructs in quantum mechanics is introduced to clarify the foundations of quantum mechanics and to explain the counter-intuitive construction of nature in quantum mechanics. The Theoretical Foundations of Quantum Mechanics is aimed at the advanced undergraduate and a...
Noncommutative Quantum Mechanics and Quantum Cosmology
Bastos, Catarina; Dias, Nuno; Prata, Joao Nuno
2009-01-01
We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity between momenta is shown to be relevant. We also discuss some qualitative features of the GQW such as the Berry phase. In the context of quantum cosmology we consider a Kantowski-Sachs cosmological model and obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten (SW) map. The WDW equation is explicitly dependent on the noncommutative parameters, $\\theta$ and $\\eta$. We obtain numerical solutions of the noncommutative WDW equation for different values of the noncommutative parameters. We conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommmutativity can be relevant for a selection of possible initial states for the universe.
Principles of Quantum Mechanics
Landé, Alfred
2013-10-01
ödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.
Quantum mechanics & the big world
Wezel, Jasper van
2007-01-01
Quantum Mechanics is one of the most successful physical theories of the last century. It explains physical phenomena from the smallest to the largest lengthscales. Despite this triumph, quantum mechanics is often perceived as a mysterious theory, involving superposition states that are alien to our
Discovering Quantum Mechanics Once Again
Duck, Ian M
2003-01-01
We expand on a recent development by Hardy, in which quantum mechanics is derived from classical probability theory supplemented by a single new axiom, Hardy's Axiom 5. Our scenario involves a `pretend world' with a `pretend' Heisenberg who seeks to construct a dynamical theory of probabilities and is lead -- seemingly inevitably -- to the Principles of Quantum Mechanics.
Quantum mechanics & the big world
Wezel, Jasper van
2007-01-01
Quantum Mechanics is one of the most successful physical theories of the last century. It explains physical phenomena from the smallest to the largest lengthscales. Despite this triumph, quantum mechanics is often perceived as a mysterious theory, involving superposition states that are alien to our
Quantum mechanics of molecular structures
Yamanouchi, Kaoru
2012-01-01
At a level accessible to advanced undergraduates, this textbook explains the fundamental role of quantum mechanics in determining the structure, dynamics, and other properties of molecules. Readers will come to understand the quantum-mechanical basis for harmonic oscillators, angular momenta and scattering processes. Exercises are provided to help readers deepen their grasp of the essential phenomena.
On Finite $J$-Hermitian Quantum Mechanics
Lee, Sungwook
2014-01-01
In his recent paper arXiv:1312.7738, the author discussed $J$-Hermitian quantum mechanics and showed that $PT$-symmetric quantum mechanics is essentially $J$-Hermitian quantum mechanics. In this paper, the author discusses finite $J$-Hermitian quantum mechanics which is derived naturally from its continuum one and its relationship with finite $PT$-symmetric quantum mechanics.
Modern Approach to Quantum Mechanics
Townsend, John S.
Inspired by Richard Feynman and J.J. Sakurai, A Modern Approach to Quantum Mechanics lets professors expose their undergraduates to the excitement and insight of Feynman's approach to quantum mechanics while simultaneously giving them a textbook that is well-ordered, logical, and pedagogically sound. This book covers all the topics that are typically presented in a standard upper-level course in quantum mechanics, but its teaching approach is new: Rather than organizing his book according to the historical development of the field and jumping into a mathematical discussion of wave mechanics, Townsend begins his book with the quantum mechanics of spin. Thus, the first five chapters of the book succeed in laying out the fundamentals of quantum mechanics with little or no wave mechanics, so the physics is not obscured by mathematics. Starting with spin systems gives students something new and interesting while providing elegant but straightforward examples of the essential structure of quantum mechanics. When wave mechanics is introduced later, students perceive it correctly as only one aspect of quantum mechanics and not the core of the subject. Praised for its pedagogical brilliance, clear writing, and careful explanations, this book is destined to become a landmark text.
Cruz, Víctor; Ramos, Javier; Martínez-Salazar, Javier
2011-04-28
An exhaustive umbrella sampling simulation of the alanine dipeptide in solution is reported. The presence of stable Y conformations in solution is assessed by both quantum calculations and experimental data from X-ray and NMR protein-solved structures available in the protein coil library. The agreement between experimental and simulation Ramachandran plots of the dipeptide in solution is excellent. A suitable explanation of the stabilization of the Y conformation mediated by water for the alanine dipeptide is discussed on the basis of Car-Parrinello MD calculations of the dipeptide in water.
Cheng, Tao; Xiao, Hai; Goddard, William A
2016-10-11
Copper is the only elemental metal that reduces a significant fraction of CO2 to hydrocarbons and alcohols, but the atomistic reaction mechanism that controls the product distributions are not known because it has not been possible to detect the reaction intermediates on the electrode surface experimentally, or carry out Quantum Mechanics (QM) calculations with a realistic description of the electrolyte (water). Here, we carry out Quantum Mechanics (QM) calculations with an explicit description of water on the Cu(100) surface (experimentally shown to be stable under CO2RR conditions) to examine the initial reaction pathways to form CO and formate (HCOO(-)) from CO2 through free energy calculations at 298K and pH 7. We find that CO formation proceeds from physisorbed CO2 to chemisorbed CO2 (*CO2(δ-)), with a free energy barrier of ΔG(‡)=0.43 eV, the rate determining step (RDS). The subsequent barriers of protonating *CO2(δ-) to form COOH* and then dissociating COOH* to form *CO are 0.37 eV and 0.30 eV, respectively. HCOO(-) formation proceeds through a very different pathway in which physisorbed CO2 reacts directly with a surface H* (along with electron transfer), leading to ΔG(‡) = 0.80 eV. Thus, the competition between CO formation and HCOO(-) formation occurs in the first electron transfer step. On Cu(100), the RDS for CO formation is lower, making CO the predominant product. Thus, to alter the product distribution we need to control this first step of CO2 binding, which might involve alloying or changing the structure at the nanoscale.
Quantum Mechanical Studies of DNA and LNA
DEFF Research Database (Denmark)
Koch, Troels; Shim, Irene; Lindow, Morten;
2014-01-01
Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies of the e......Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies...
Sawada, Toshihiko; Fedorov, Dmitri G; Kitaura, Kazuo
2010-12-01
The selective binding between avian and human influenza A viral hemagglutinins (HA) subtype H3 and Neu5Acα2-3 and α2-6Gal (avian α2-3, human α2-6) is qualitatively rationalized by the fragment molecular orbital (FMO) method. We suggest a general model of analyzing protein-ligand interactions based on the electrostatic, polarization, dispersion, and desolvation components obtained from quantum-mechanical calculations at the MP2/6-31G(d) level with the polarizable continuum model of solvation. The favorable avian H3 (A/duck/Ukraine/1963)-avian α2-3 binding arises from the hydrophilic interaction between Gal-4 OH and side-chain NH(2)CO on Gln226, which is supported by the intermolecular hydrogen-bond network to the 1-COO group on Neu5Ac moiety. A substitution of Gln226Leu in the avian H3 HA1 domain increases the binding affinity to human α2-6 due to the Leu226···human α2-6 dispersion with a small entropic penalty during the complex formation. The remarkable human H3 (A/Aichi/2/1968)-human α2-6 binding is not governed by the Ser228-OH···OH-9 Neu5Ac hydrogen bond. These fragment-based chemical aspects can help design monovalent inhibitors of the influenza viral HA-sialoside binding and the simulation studies on the viral HAs-human α2-6 binding.
Quantum mechanics in complex systems
Hoehn, Ross Douglas
This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown
Mathematical foundation of quantum mechanics
Parthasarathy, K R
2005-01-01
This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations ...
Quantum mechanics a modern development
Ballentine, Leslie E
2015-01-01
Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory. In this edition a new chapter on quantum information is added. As the topic is still in a state of rapid development, a comprehensive treatment is not feasible. The emphasis is on the fundamental principles and some key applications, including quantum cryptography, teleportation of states, and quantum computing. The impact of quantum information theory on the foundations of quantum mechanics is discussed. In addition, there are minor revisions ...
Efficient calculation of dissipative quantum transport properties in semiconductor nanostructures
Energy Technology Data Exchange (ETDEWEB)
Greck, Peter
2012-11-26
We present a novel quantum transport method that follows the non-equilibrium Green's function (NEGF) framework but side steps any self-consistent calculation of lesser self-energies by replacing them by a quasi-equilibrium expression. We termed this method the multi-scattering Buettiker-Probe (MSB) method. It generalizes the so-called Buettiker-Probe model but takes into account all relevant individual scattering mechanisms. It is orders of magnitude more efficient than a fully selfconsistent non-equilibrium Green's function calculation for realistic devices, yet accurately reproduces the results of the latter method as well as experimental data. This method is fairly easy to implement and opens the path towards realistic three-dimensional quantum transport calculations. In this work, we review the fundamentals of the non-equilibrium Green's function formalism for quantum transport calculations. Then, we introduce our novel MSB method after briefly reviewing the original Buettiker-Probe model. Finally, we compare the results of the MSB method to NEGF calculations as well as to experimental data. In particular, we calculate quantum transport properties of quantum cascade lasers in the terahertz (THz) and the mid-infrared (MIR) spectral domain. With a device optimization algorithm based upon the MSB method, we propose a novel THz quantum cascade laser design. It uses a two-well period with alternating barrier heights and complete carrier thermalization for the majority of the carriers within each period. We predict THz laser operation for temperatures up to 250 K implying a new temperature record.
Communication: quantum mechanics without wavefunctions.
Schiff, Jeremy; Poirier, Bill
2012-01-21
We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications-theoretical, computational, and interpretational-are discussed.
Coherent states in quantum mechanics
Rodrigues, R D L; Fernandes, D
2001-01-01
We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out.
Yang, Huan; Han, Ke-Li; Nanbu, Shinkoh; Nakamura, Hiroki; Balint-Kurti, Gabriel G; Zhang, Hong; Smith, Sean C; Hankel, Marlies
2008-08-28
OCl/OH product branching ratios are calculated as a function of total energy for the O( (1) D) + HCl reaction using quantum wavepacket methods. The calculations take account of reaction on all the three electronic state potential energy surfaces which correlate with both reactants and products. Our results show that reaction on the excited electronic state surfaces has a large effect on the branching ratio at higher energies and that these surfaces must therefore be fully taken into account. The calculations use the potential energy surfaces of Nanbu and co-workers. Product vibrational and rotational quantum state distributions are also calculated as a function of energy for both product channels. Inclusion of the excited electronic state potential energy surfaces improves the agreement of the predicted product vibrational quantum state distributions with experiment for the OH product channel. For OCl agreement between theory and experiment is retained for the vibrational quantum state distributions when the excited electronic state potential energy surfaces are included in the analysis. For the rotational state distributions good agreement between theory and experiment is maintained for energies at which experimental results are available. At higher energies, above 0.7 eV of total energy, the OCl rotational state distributions predicted using all three electronic state potential energy surfaces shift to markedly smaller rotational quantum numbers.
Computations in quantum mechanics made easy
Korsch, H. J.; Rapedius, K.
2016-09-01
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.
Quantum Mechanics of Extended Objects
Sastry, R R
2000-01-01
We propose a quantum mechanics of extended objects that accounts for the finite extent of a particle defined via its Compton wavelength. The Hilbert space representation theory of such a quantum mechanics is presented and this representation is used to demonstrate the quantization of spacetime. The quantum mechanics of extended objects is then applied to two paradigm examples, the fuzzy (extended object) harmonic oscillator and the Yukawa potential. In the second example the phenomenological coupling constant of the $\\omega$ meson which mediates the short range and repulsive nucleon force as well as the repulsive core radius are theoretically predicted.
Quantum mechanics in Hilbert space
Prugovecki, Eduard
2006-01-01
A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas.This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the
Linear operators for quantum mechanics
Jordan, Thomas F
2006-01-01
This compact treatment highlights the logic and simplicity of the mathematical structure of quantum mechanics. Suitable for advanced undergraduates and graduate students, it treats the language of quantum mechanics as expressed in the mathematics of linear operators.Originally oriented toward atomic physics, quantum mechanics became a basic language for solid-state, nuclear, and particle physics. Its grammar consists of the mathematics of linear operators, and with this text, students will find it easier to understand and use the language of physics. Topics include linear spaces and linear fun
Stochastic methods in quantum mechanics
Gudder, Stanley P
2005-01-01
Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun
Quantum mechanical irreversibility and measurement
Grigolini, P
1993-01-01
This book is intended as a tutorial approach to some of the techniques used to deal with quantum dissipation and irreversibility, with special focus on their applications to the theory of measurements. The main purpose is to provide readers without a deep expertise in quantum statistical mechanics with the basic tools to develop a critical judgement on whether the major achievements in this field have to be considered a satisfactory solution of quantum paradox, or rather this ambitious achievement has to be postponed to when a new physics, more general than quantum and classical physics, will
Time Asymmetric Quantum Mechanics
National Research Council Canada - National Science Library
Arno R Bohm; Manuel Gadella; Piotr Kielanowski
2011-01-01
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1...
Relativistic quantum mechanics
Horwitz, Lawrence P
2015-01-01
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...
Analytical mechanics for relativity and quantum mechanics
Johns, Oliver Davis
2011-01-01
Analytical Mechanics for Relativity and Quantum Mechanics is an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the introductory graduate level. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum...
Hilbert space and quantum mechanics
Gallone, Franco
2015-01-01
The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Pref...
Quantum mechanics principles and formalism
McWeeny, Roy
2012-01-01
Focusing on main principles of quantum mechanics and their immediate consequences, this graduate student-oriented volume develops the subject as a fundamental discipline, opening with review of origins of Schrödinger's equations and vector spaces.
Quantum mechanical description of waveguides
Institute of Scientific and Technical Information of China (English)
Wang Zhi-Yong; Xiong Cai-Dong; He Bing
2008-01-01
Applying the spinor representation of the electromagnetic field,this paper present a quantum-mechanical description of waveguides.As an example of application,a potential qubit generated by photon tunnelling is discussed.
Quantum Mechanics and Common Sense
Gantsevich, S V
2016-01-01
A physical picture for Quantum Mechanics which permits to conciliate it with the usual common sense is proposed. The picture agrees with the canonical Copenhagen interpretation making more clear its statements.
Quantum mechanics I the fundamentals
Rajasekar, S
2015-01-01
Quantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels. It covers basic concepts, mathematical formalism, and applications to physically important systems.
Directory of Open Access Journals (Sweden)
Simone Di Micco
2013-12-01
Full Text Available In this paper the stereostructural investigation of two new oxygenated polyketides, plakilactones G and H, isolated from the marine sponge Plakinastrella mamillaris collected at Fiji Islands, is reported. The stereostructural studies began on plakilactone H by applying an integrated approach of the NOE-based protocol and quantum mechanical calculations of 13C chemical shifts. In particular, plakilactone H was used as a template to extend the application of NMR-derived interproton distances to a highly flexible molecular system with simultaneous assignment of four non-contiguous stereocenters. Chemical derivatization and quantum mechanical calculations of 13C on plakilactone G along with a plausible biogenetic interconversion between plakilactone G and plakilactone H allowed us to determine the absolute configuration in this two new oxygenated polyketides.
Nakamura, Shin; Ota, Kai; Shibuya, Yuichi; Noguchi, Takumi
2016-01-26
Photosynthetic water oxidation takes place at the Mn4CaO5 cluster in photosystem II. Around the Mn4CaO5 cluster, a hydrogen bond network is formed by several water molecules, including four water ligands. To clarify the role of this water network in the mechanism of water oxidation, we investigated the effects of the removal of Ca(2+) and substitution with metal ions on the vibrations of water molecules coupled to the Mn4CaO5 cluster by means of Fourier transform infrared (FTIR) difference spectroscopy and quantum mechanics/molecular mechanics (QM/MM) calculations. The OH stretching vibrations of nine water molecules forming a network between D1-D61 and YZ were calculated using the QM/MM method. On the the calculated normal modes, a broad positive feature at 3200-2500 cm(-1) in an S2-minus-S1 FTIR spectrum was attributed to the vibrations of strongly hydrogen-bonded OH bonds of water involving the vibrations of water ligands to a Mn ion and the in-phase coupled vibration of a water network connected to YZ, while bands in the 3700-3500 cm(-1) region were assigned to the coupled vibrations of weakly hydrogen-bonded OH bonds of water. All the water bands were lost upon Ca(2+) depletion and Ba(2+) substitution, which inhibit the S2 → S3 transition, indicating that a solid water network was broken by these treatments. By contrast, Sr(2+) substitution slightly altered the water bands around 3600 cm(-1), reflecting minor modification in water interactions, consistent with the retention of water oxidation activity with a decreased efficiency. These results suggest that the water network around the Mn4CaO5 cluster plays an essential role in the water oxidation mechanism particularly in a concerted process of proton transfer and water insertion during the S2 → S3 transition.
Farahani, Pooria; Lundberg, Marcus; Karlsson, Hans O.
2013-11-01
The SN2 substitution reactions at phosphorus play a key role in organic and biological processes. Quantum molecular dynamics simulations have been performed to study the prototype reaction Cl-+PH2Cl→ClPH2+Cl-, using one and two-dimensional models. A potential energy surface, showing an energy well for a transition complex, was generated using ab initio electronic structure calculations. The one-dimensional model is essentially reflection free, whereas the more realistic two-dimensional model displays involved resonance structures in the reaction probability. The reaction rate is almost two orders of magnitude smaller for the two-dimensional compared to the one-dimensional model. Energetic errors in the potential energy surface is estimated to affect the rate by only a factor of two. This shows that for these types of reactions it is more important to increase the dimensionality of the modeling than to increase the accuracy of the electronic structure calculation.
Quantum Statistical Calculation of Exchange Bias
Institute of Scientific and Technical Information of China (English)
WANG Huai-Yu; DAI Zhen-Hong
2004-01-01
The phenomenon of exchange bias of ferromagnetic (FM) films, which are coupled with an antiferromagnetic (AFM) film, is studied by Heisenberg model by use of the many-body Green's function method of quantum statistical theory for the uncompensated case. Exchange bias HE and coercivity Hc are calculated as functions of the FM film thickness L, temperature, the strength of the exchange interaction across the interface between FM and AFM and the anisotropy of the FM. Hc decreases with increasing L when the FM film is beyond some thickness. The dependence of the exchange bias HE on the FM film thickness and on temperature is also qualitatively in agreement with experiments.
The physics of quantum mechanics
Binney, James
2014-01-01
The Physics of Quantum Mechanics aims to give students a good understanding of how quantum mechanics describes the material world. It shows that the theory follows naturally from the use of probability amplitudes to derive probabilities. It stresses that stationary states are unphysical mathematical abstractions that enable us to solve the theory's governing equation, the time-dependent Schroedinger equation. Every opportunity is taken to illustrate the emergence of the familiarclassical, dynamical world through the quantum interference of stationary states. The text stresses the continuity be
Quantum mechanics in a nutshell
Mahan, Gerald D
2009-01-01
Covering the fundamentals as well as many special topics of current interest, this is the most concise, up-to-date, and accessible graduate-level textbook on quantum mechanics available. Written by Gerald Mahan, a distinguished research physicist and author of an acclaimed textbook on many-particle physics, Quantum Mechanics in a Nutshell is the distillation of many years' teaching experience. Emphasizing the use of quantum mechanics to describe actual quantum systems such as atoms and solids, and rich with interesting applications, the book proceeds from solving for the properties of a single particle in potential; to solving for two particles (the helium atom); to addressing many-particle systems. Applications include electron gas, magnetism, and Bose-Einstein Condensation; examples are carefully chosen and worked; and each chapter has numerous homework problems, many of them original
Bulut, Niyazi; Kłos, Jacek; Roncero, Octavio
2015-06-07
We present accurate state-to-state quantum wave packet calculations of integral cross sections and rate constants for the title reaction. Calculations are carried out on the best available ground 1(2)A' global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged state-to-state reaction cross sections have been calculated for collision energies up to 0.5 eV and different initial rotational and vibrational excitations, DCl(v = 0, j = 0 - 1; v = 1, j = 0). Also, initial-state resolved rate constants of the title reaction have been calculated in a temperature range of 100-400 K. It is found that the initial rotational excitation of the DCl molecule does not enhance reactivity, in contract to the reaction with the isotopologue HCl in which initial rotational excitation produces an important enhancement. These differences between the isotopologue reactions are analyzed in detail and attributed to the presence of resonances for HCl(v = 0, j), absent in the case of DCl(v = 0, j). For vibrational excited DCl(v = 1, j), however, the reaction cross section increases noticeably, what is also explained by another resonance.
Mathematical foundations of quantum mechanics
Mackey, George W
2004-01-01
Designed for students familiar with abstract mathematical concepts but possessing little knowledge of physics, this text focuses on generality and careful formulation rather than problem-solving. Its author, a member of the distinguished National Academy of Science, based this graduate-level text on the course he taught at Harvard University.Opening chapters on classical mechanics examine the laws of particle mechanics; generalized coordinates and differentiable manifolds; oscillations, waves, and Hilbert space; and statistical mechanics. A survey of quantum mechanics covers the old quantum
Quantum Mechanics and determinism
Hooft, G. 't
2001-01-01
It is shown how to map the quantum states of a system of free scalar particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group. The mapping is now also applied to free Maxwell fields. Lorentz invariance is demonstrated.
The quantum field theory interpretation of quantum mechanics
de la Torre, Alberto C.
2015-01-01
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
Quantum Mechanics and Narratability
Myrvold, Wayne C.
2016-07-01
As has been noted by several authors, in a relativistic context, there is an interesting difference between classical and quantum state evolution. For a classical system, a state history of a quantum system given along one foliation uniquely determines, without any consideration of the system's dynamics, a state history along any other foliation. This is not true for quantum state evolution; there are cases in which a state history along one foliation is compatible with multiple distinct state histories along some other, a phenomenon that David Albert has dubbed "non-narratability." In this article, we address the question of whether non-narratability is restricted to the sorts of special states that so far have been used to illustrate it. The results of the investigation suggest that there has been a misplaced emphasis on underdetermination of state histories; though this is generic for the special cases that have up until now been considered, involving bipartite systems in pure entangled states, it fails generically in cases in which more component systems are taken into account, and for bipartite systems that have some entanglement with their environment. For such cases, if we impose relativistic causality constraints on the evolution, then, except for very special states, a state history along one foliation uniquely determines a state history along any other. But this in itself is a marked difference between classical and quantum state evolution, because, in a classical setting, no considerations of dynamics at all are needed to go from a state history along one foliation to a state history along another.
Mátyus, Edit; Reiher, Markus
2012-07-14
We elaborate on the theory for the variational solution of the Schrödinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schrödinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H(2) (+) and H(2), three bound states of the positronium molecule, Ps(2), and the ground and two excited states of the (7)Li atom.
Tantillo, Dean J
2013-08-01
This Highlight describes applications of quantum chemical calculations to problems in natural products chemistry, including the elucidation of natural product structures (distinguishing between constitutional isomers, distinguishing between diastereomers, and assigning absolute configuration) and determination of reasonable mechanisms for their formation.
Quantum Mechanical Earth: Where Orbitals Become Orbits
Keeports, David
2012-01-01
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
Quantum Mechanical Earth: Where Orbitals Become Orbits
Keeports, David
2012-01-01
Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…
QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.
Wollman, E E; Lei, C U; Weinstein, A J; Suh, J; Kronwald, A; Marquardt, F; Clerk, A A; Schwab, K C
2015-08-28
According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion.
Framing difficulties in quantum mechanics
Modir, Bahar; Sayre, Eleanor C
2016-01-01
Students' difficulties in quantum mechanics may be the result of unproductive framing and not fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics problems in an upper-division physics course. Using the lens of the epistemological framing, we investigated four frames in our observational data: algorithmic math, conceptual math, algorithmic physics, and conceptual physics. We then used our framework to seek an underlying structure to the long lists of published difficulties that span many topics in quantum mechanics. We mapped descriptions of published difficulties into errors in epistemological framing and resource use. We analyzed descriptions of students' problem solving to find their frames, and compared students' framing to framing (and frame shifting) required by problem statements. We found three categories of error: mismatches between students' framing and problem statement framing; inappropriate or absent transiti...
Algebraic Quantum Mechanics and Pregeometry
Hiley, D J B P G D B J
2006-01-01
We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford Algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra in a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra.
Remarks on osmosis, quantum mechanics, and gravity
Carroll, Robert
2011-01-01
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and superfluids with connections to gravity.
Black holes and quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hooft, G. ' t, E-mail: g.thooft@uu.n [Institute for Theoretical Physics, Utrecht University and Spinoza Institute, P.O. Box 80.195, 3508 TD Utrecht (Netherlands)
2010-07-15
After a brief review of quantum black hole physics, it is shown how the dynamical properties of a quantum black hole may be deduced to a large extent from Standard Model Physics, extended to scales near the Planck length, and combined with results from perturbative quantum gravity. Together, these interactions generate a Hilbert space of states on the black hole horizon, which can be investigated, displaying interesting systematics by themselves. To make such approaches more powerful, a study is made of the black hole complementarity principle, from which one may deduce the existence of a hidden form of local conformal invariance. Finally, the question is raised whether the principles underlying Quantum Mechanics are to be sharpened in this domain of physics as well. There are intriguing possibilities.
Quantum mechanical studies of carbon structures
Energy Technology Data Exchange (ETDEWEB)
Bartelt, Norman Charles [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Ward, Donald [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Zhou, Xiaowang [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Foster, Michael E. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Schultz, Peter A. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Wang, Bryan M. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Univ. of California, Riverside, CA (United States); McCarty, Kevin F. [Sandia National Lab. (SNL-CA), Livermore, CA (United States)
2015-10-01
Carbon nanostructures, such as nanotubes and graphene, are of considerable interest due to their unique mechanical and electrical properties. The materials exhibit extremely high strength and conductivity when defects created during synthesis are minimized. Atomistic modeling is one technique for high resolution studies of defect formation and mitigation. To enable simulations of the mechanical behavior and growth mechanisms of C nanostructures, a high-fidelity analytical bond-order potential for the C is needed. To generate inputs for developing such a potential, we performed quantum mechanical calculations of various C structures.
BOOK REVIEWS: Quantum Mechanics: Fundamentals
Whitaker, A.
2004-02-01
. It has a restricted range of general topics, and consists of three parts entitled `Nonrelativistic Many-Particle Systems', `Relativistic Wave Equations', and `Relativistic Fields'. Thus it studies in some depth areas of physics which are either dealt with in an introductory fashion, or not reached at all, by Gottfried and Yan. Despite its more advanced level, this book may actually be the more accessible to an isolated learner, because the various aspects are developed in an unhurried fashion; the author remarks that ‘the inclusion of all mathematical steps and full presentation of intermediate calculations ensures ease of understanding’. Many useful student problems are included. The presentation is said to be rigorous, but again this is a book for the physicist rather than the mathematician. The treatment of many-particle systems begins with a rather general introduction to second quantization, and then applies this formalism to spin-1/2 fermions and bosons. The study of fermions includes consideration of the Fermi sphere, the electron gas, and the Hartree--Fock equations for atoms; that of bosons includes Bose--Einstein condensation, Bogoliubov theory of the weakly interacting Bose gas, and a brief account of superfluidity. The last section of this part of the book investigates in detail the dynamics of many-particle systems on a microscopic quantum-mechanical basis using, in particular, the dynamical correlation functions. In the second part which considers relativistic wave equations, the Klein--Gordon and Dirac equations are derived, and the Lorentz covariance of the Dirac equation is established. The role of angular momentum in relativistic quantum mechanics is explained, as a preliminary to the study of the energy levels in a Coulomb potential using both the Klein--Gordon and Dirac equations, the latter being solved exactly for the hydrogen atom. For larger atoms, the Foldy--Wouthuysen transformation is explained, and also relativistic corrections and the
Quantum mechanics foundations and applications
Swanson, Donald Gary
2006-01-01
Progressing from the fundamentals of quantum mechanics (QM) to more complicated topics, Quantum Mechanics: Foundations and Applications provides advanced undergraduate and graduate students with a comprehensive examination of many applications that pertain to modern physics and engineering.Based on courses taught by the author, this textbook begins with an introductory chapter that reviews historical landmarks, discusses classical theory, and establishes a set of postulates. The next chapter demonstrates how to find the appropriate wave functions for a variety of physical systems in one dimens
Lecture Script: Introduction to Computational Quantum Mechanics
Schmied, Roman
2014-01-01
This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013. It is aimed at advanced students of physics who are familiar with the concepts and notations of quantum mechanics. Quantum mechanics lectures can often be separated into two classes. In the first class you get to know Schroedinger's equation and find the form and dynamics of simple physical systems (square well, harmonic oscillator, hydrogen atom); most calculations are analytic and inspired by calculations originally done in the 1920s and 1930s. In the second class you learn about large systems such as molecular structures, crystalline solids, or lattice models; these calculations are usually so complicated that it is difficult for the student to understand them in all detail. This lecture tries to bridge the gap between simple analytic calculations and complicated large-scale computations. We will revisit most of the problems encountered in introductory quantum mechanics, fo...
Quantum Mechanics/Molecular Mechanics Modeling of Drug Metabolism
DEFF Research Database (Denmark)
Lonsdale, Richard; Fort, Rachel M; Rydberg, Patrik;
2016-01-01
The mechanism of cytochrome P450(CYP)-catalyzed hydroxylation of primary amines is currently unclear and is relevant to drug metabolism; previous small model calculations have suggested two possible mechanisms: direct N-oxidation and H-abstraction/rebound. We have modeled the N-hydroxylation of (R......)-mexiletine in CYP1A2 with hybrid quantum mechanics/molecular mechanics (QM/MM) methods, providing a more detailed and realistic model. Multiple reaction barriers have been calculated at the QM(B3LYP-D)/MM(CHARMM27) level for the direct N-oxidation and H-abstraction/rebound mechanisms. Our calculated barriers...... indicate that the direct N-oxidation mechanism is preferred and proceeds via the doublet spin state of Compound I. Molecular dynamics simulations indicate that the presence of an ordered water molecule in the active site assists in the binding of mexiletine in the active site...
Quantum Monte Carlo Calculations of Neutron Matter
Carlson, J; Ravenhall, D G
2003-01-01
Uniform neutron matter is approximated by a cubic box containing a finite number of neutrons, with periodic boundary conditions. We report variational and Green's function Monte Carlo calculations of the ground state of fourteen neutrons in a periodic box using the Argonne $\\vep $ two-nucleon interaction at densities up to one and half times the nuclear matter density. The effects of the finite box size are estimated using variational wave functions together with cluster expansion and chain summation techniques. They are small at subnuclear densities. We discuss the expansion of the energy of low-density neutron gas in powers of its Fermi momentum. This expansion is strongly modified by the large nn scattering length, and does not begin with the Fermi-gas kinetic energy as assumed in both Skyrme and relativistic mean field theories. The leading term of neutron gas energy is ~ half the Fermi-gas kinetic energy. The quantum Monte Carlo results are also used to calibrate the accuracy of variational calculations ...
Effective equations for the quantum pendulum from momentous quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)
2012-08-24
In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Quantum Mechanics, is it magic
Ferrero, M; Sánchez-Gómez, J L
2008-01-01
We show that quantum mechanics is the first theory in human history that violates the basic a priori principles that have shaped human thought since immemorial times. Therefore although it is more contrary to magic than any body of knowledge could be, what could be called its magic precisely resides in this violation.
Mind, matter and quantum mechanics
Stapp, Henry P
2009-01-01
"Scientists other than quantum physicists often fail to comprehend the enormity of the conceptual change wrought by quantum theory in our basic conception of the nature of matter," writes Henry Stapp. Stapp is a leading quantum physicist who has given particularly careful thought to the implications of the theory that lies at the heart of modern physics. In this book, which contains several of his key papers as well as new material, he focuses on the problem of consciousness and explains how quantum mechanics allows causally effective conscious thought to be combined in a natural way with the physical brain made of neurons and atoms. The book is divided into four sections. The first consists of an extended introduction. Key foundational and somewhat more technical papers are included in the second part, together with a clear exposition of the "orthodox" interpretation of quantum mechanics. The third part addresses, in a non-technical fashion, the implications of the theory for some of the most profound questi...
Philosophic foundations of quantum mechanics
Reichenbach, Hans
1998-01-01
Physics concerns direct analysis of the physical world, while philosophy analyzes knowledge about the physical world. This volume combines both disciplines for a philosophical interpretation of quantum physics - an interpretation free from the imprecision of metaphysics, offering a view of the atomic world and its quantum mechanical results as concrete as the visible everyday world.Written by an internationally renowned philosopher who specialized in symbolic logic and the theory of relativity, this approach consists of three parts. The first section, which requires no background in math or p
Memetics of Quantum Mechanical Interpretations
Chakrabarty, I
2006-01-01
Memes, self reproducing mental information and cognitive structures analogous to genes in biology, can be seen as the basis for an explanatory model of cultural and psychological behavior. Their properties and effects are evolutionary conditioned and ultimately seeks to promote their replication. To survive in a context the memes must meet certain conditions. We here propose a Memetics of Quantum Mechanical Interpretations, which have eluded mankind for a century now. We also see how the ideas of memes best fit the way scientific theories in general and Quantum Theory in particular propagates in the scientific brains and finds its expressions in the scientific community and effects the way we perceive Nature.
Operator methods in quantum mechanics
Schechter, Martin
2003-01-01
This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing q
Wigner distributions in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ercolessi, E; Marmo, G; Morandi, G; Mukunda, N [Physics Department, University of Bologna, INFN and CNISM. 46 v.Irnerio. I-40126, Bologna (Italy); Dip. di Scienze Fisiche. University di Napoli ' Federico II' and INFN. v.Cinzia. I-80100 Naples (Italy); Physics Department, University of Bologna, INFN and CNISM. 6/2 v.le Berti Pichat. I-40127, Bologna (Italy); Centre for High-Energy Physics. Indian Institute of Science. Bamgalore 560012 (India)
2007-11-15
The Weyl-Wigner description of quantum mechanical operators and states in classical phase-space language is well known for Cartesian systems. We describe a new approach based on ideas of Dirac which leads to the same results but with interesting additional insights. A way to set up Wigner distributions in an interesting non-Cartesian case, when the configuration space is a compact connected Lie group, is outlined. Both these methods are adapted to quantum systems with finite-dimensional Hilbert spaces, and the results are contrasted.
Paradoxical reflection in quantum mechanics
Pedro L. Garrido; Goldstein, Sheldon; Lukkarinen, Jani; Tumulka, Roderich
2011-01-01
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This p...
Making sense of quantum mechanics
Bricmont, Jean
2016-01-01
This book explains, in simple terms, with a minimum of mathematics, why things can appear to be in two places at the same time, why correlations between simultaneous events occurring far apart cannot be explained by local mechanisms, and why, nevertheless, the quantum theory can be understood in terms of matter in motion. No need to worry, as some people do, whether a cat can be both dead and alive, whether the moon is there when nobody looks at it, or whether quantum systems need an observer to acquire definite properties. The author’s inimitable and even humorous style makes the book a pleasure to read while bringing a new clarity to many of the longstanding puzzles of quantum physics.
The Lagrangian in Quantum Mechanics
Dirac, P. A. M.
Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue, as a result of which the whole of the classical Hamiltonian theory, which is just a structure built up on this notion, could be taken over in all its details into quantum mechanics. Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental. In the first place the Lagrangian method allows one to collect together all the equations of motion and express them as the stationary property of a certain action function. (This action function is just the time-integral of the Lagrangian.) There is no corresponding action principle in terms of the coordinates and momenta of the Hamiltonian theory. Secondly the Lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; while the Hamiltonian method is essentially non-relativistic in form, since it marks out a particular time variable as the canonical conjugate of the Hamiltonian function. For these reasons it would seem desirable to take up the question of what corresponds in the quantum theory to the Lagrangian method of the classical theory. A little consideration shows, however, that one cannot expect to be able to take over the classical Lagrangian equations in any very direct way. These equations involve partial derivatives of the Lagrangian with respect to the coordinates and velocities and no meaning can be given to such derivatives in quantum mechanics. The only differentiation process that can be carried out with respect to the dynamical variables of
Non-relativistic Quantum Mechanics versus Quantum Field Theories
Pineda, Antonio
2007-01-01
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
Star Products for Relativistic Quantum Mechanics
Henselder, P.
2007-01-01
The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.
Bohmian Mechanics and the Quantum Revolution
Goldstein, Sheldon
1995-01-01
This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena--...
Quantum chemical calculation of the equilibrium structures of small metal atom clusters
Kahn, L. R.
1982-01-01
Metal atom clusters are studied based on the application of ab initio quantum mechanical approaches. Because these large 'molecular' systems pose special practical computational problems in the application of the quantum mechanical methods, there is a special need to find simplifying techniques that do not compromise the reliability of the calculations. Research is therefore directed towards various aspects of the implementation of the effective core potential technique for the removal of the metal atom core electrons from the calculations.
Quantum mechanics and the psyche
Galli Carminati, G.; Martin, F.
2008-07-01
In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.
Quantum mechanics of black holes.
Witten, Edward
2012-08-03
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
Quantum communication between remote mechanical resonators
Felicetti, S.; Fedortchenko, S.; Rossi, R.; Ducci, S.; Favero, I.; Coudreau, T.; Milman, P.
2017-02-01
Mechanical resonators represent one of the most promising candidates to mediate the interaction between different quantum technologies, bridging the gap between efficient quantum computation and long-distance quantum communication. Here, we introduce an interferometric scheme where the interaction of a mechanical resonator with input-output quantum pulses is controlled by an independent classical drive. We design protocols for state teleportation and direct quantum state transfer, between distant mechanical resonators. The proposed device, feasible with state-of-the-art technology, can serve as a building block for the implementation of long-distance quantum networks of mechanical resonators.
Crum's Theorem for `Discrete' Quantum Mechanics
Odake, Satoru; Sasaki, Ryu
2009-01-01
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in `discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schr\\"odinger equation is a difference equation.
Helping Students Learn Quantum Mechanics for Quantum Computing
Singh, Chandralekha
2016-01-01
Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research in quantum computing because there is a lack of emphasis in the current curriculum on quantum formalism and dynamics. We are investigating the difficulties students have with quantum mechanics and are developing and evaluating quantum interactive learning tutorials (QuILTs) to reduce the difficulties. Our investigation includes interviews with individual students and the development and administration of free-response and multiple-choice tests. We discuss the implications of our research and development project on helping students learn quantum mechanics relevant for quantum computing.
Geometrical Phases in Quantum Mechanics
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
Supersymmetric quantum mechanics with reflections
Energy Technology Data Exchange (ETDEWEB)
Post, Sarah; Vinet, Luc [Centre de Recherches Mathematiques, Universite de Montreal, Montreal CP6128 (QC) H3C 3J7 (Canada); Zhedanov, Alexei, E-mail: post@crm.umontreal.ca, E-mail: luc.vinet@umontreal.ca, E-mail: zhedanov@fti.dn.ua [Donetsk Institute for Physics and Technology, Donetsk 83114 (Ukraine)
2011-10-28
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q {yields} -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wavefunctions of extended Scarf I potentials with different parameters are presented. (paper)
Fun with supersymmetric quantum mechanics
Freedman, B.; Cooper, F.
1984-04-01
The Hamiltonian and path integral approaches to supersymmetric quantum mechanics were reviewed. The related path integrals for the Witten Index and for stochastic processes were discussed and shown to be indications for supersymmetry breakdown. A system where in the superpotential W(x) has assymetrical values at + or - infinity was considered. Nonperturbative strategies for studying supersymmetry breakdown were described. These strategies are based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed.
Chen, Xiao; Zhao, Yanying; Zhang, Haibo; Xue, Jiadan; Zheng, Xuming
2015-02-05
The photophysics and photochemistry of thioacetamide (CH3CSNH2) after excitation to the S2 electronic state were investigated by using resonance Raman spectroscopy in conjunction with the complete active space self-consistent field (CASSCF) method and density functional theory (DFT) calculations. The A-band resonance Raman spectra in acetonitrile, methanol, and water were obtained at 299.1, 282.4, 266.0, 252.7, and 245.9 nm excitation wavelengths to probe the structural dynamics of thioacetamide in the S2 state. CASSCF calculations were done to determine the transition energies and structures of the lower-lying excited states, the conical intersection points CI(S2/S1) and CI(S1/S0), and intersystem crossing points. The structural dynamics of thioacetamide in the S2 state was revealed to be along eight Franck-Condon active vibrational modes ν15, ν11, ν14, ν10, ν8, ν12, ν18, and ν19, mostly in the CC/CS/CN stretches and the CNH8,9/CCH5,6,7/CCN/CCS in-plane bends as indicated by the corresponding normal mode descriptions. The S2 → S1 decay process via the S2/S1 conical intersection point as the major channel were excluded. The thione-thiol photoisomerization reaction mechanism of thioacetamide via the S2,FC → S'1,min excited state proton transfer (ESPT) reaction channel was proposed.
Quantum mechanical generalization of the balistic electron wind theory
Lacina, A.
1980-06-01
The Fiks' quasiclassical theory of the electron wind force is quantum mechanically generalized. Within the framework of this generalization the space dependence of the electron wind force is calculated in the vicinity of an interface between two media. It is found that quantum corrections may be comparable with or even greater than corresponding quasiclassical values.
The formalisms of quantum mechanics an introduction
David, Francois
2015-01-01
These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and ...
Transfer Area Mechanical Handling Calculation
Energy Technology Data Exchange (ETDEWEB)
B. Dianda
2004-06-23
This calculation is intended to support the License Application (LA) submittal of December 2004, in accordance with the directive given by DOE correspondence received on the 27th of January 2004 entitled: ''Authorization for Bechtel SAX Company L.L. C. to Include a Bare Fuel Handling Facility and Increased Aging Capacity in the License Application, Contract Number DE-AC28-01R W12101'' (Arthur, W.J., I11 2004). This correspondence was appended by further Correspondence received on the 19th of February 2004 entitled: ''Technical Direction to Bechtel SAIC Company L.L. C. for Surface Facility Improvements, Contract Number DE-AC28-OIRW12101; TDL No. 04-024'' (BSC 2004a). These documents give the authorization for a Fuel Handling Facility to be included in the baseline. The purpose of this calculation is to establish preliminary bounding equipment envelopes and weights for the Fuel Handling Facility (FHF) transfer areas equipment. This calculation provides preliminary information only to support development of facility layouts and preliminary load calculations. The limitations of this preliminary calculation lie within the assumptions of section 5 , as this calculation is part of an evolutionary design process. It is intended that this calculation is superseded as the design advances to reflect information necessary to support License Application. The design choices outlined within this calculation represent a demonstration of feasibility and may or may not be included in the completed design. This calculation provides preliminary weight, dimensional envelope, and equipment position in building for the purposes of defining interface variables. This calculation identifies and sizes major equipment and assemblies that dictate overall equipment dimensions and facility interfaces. Sizing of components is based on the selection of commercially available products, where applicable. This is not a specific recommendation for the future use
New methods for quantum mechanical reaction dynamics
Energy Technology Data Exchange (ETDEWEB)
Thompson, Ward Hugh [Univ. of California, Berkeley, CA (United States). Dept. of Chemistry
1996-12-01
Quantum mechanical methods are developed to describe the dynamics of bimolecular chemical reactions. We focus on developing approaches for directly calculating the desired quantity of interest. Methods for the calculation of single matrix elements of the scattering matrix (S-matrix) and initial state-selected reaction probabilities are presented. This is accomplished by the use of absorbing boundary conditions (ABC) to obtain a localized (L^{2}) representation of the outgoing wave scattering Green`s function. This approach enables the efficient calculation of only a single column of the S-matrix with a proportionate savings in effort over the calculation of the entire S-matrix. Applying this method to the calculation of the initial (or final) state-selected reaction probability, a more averaged quantity, requires even less effort than the state-to-state S-matrix elements. It is shown how the same representation of the Green`s function can be effectively applied to the calculation of negative ion photodetachment intensities. Photodetachment spectroscopy of the anion ABC^{-} can be a very useful method for obtaining detailed information about the neutral ABC potential energy surface, particularly if the ABC^{-} geometry is similar to the transition state of the neutral ABC. Total and arrangement-selected photodetachment spectra are calculated for the H_{3}O^{-} system, providing information about the potential energy surface for the OH + H_{2} reaction when compared with experimental results. Finally, we present methods for the direct calculation of the thermal rate constant from the flux-position and flux-flux correlation functions. The spirit of transition state theory is invoked by concentrating on the short time dynamics in the area around the transition state that determine reactivity. These methods are made efficient by evaluating the required quantum mechanical trace in the basis of eigenstates of the
Trace anomalies from quantum mechanics
Bastianelli, F; Bastianelli, Fiorenzo; Nieuwenhuizen, Peter van
1993-01-01
The 1-loop anomalies of a d-dimensional quantum field theory can be computed by evaluating the trace of the regulated path integral jacobian matrix, as shown by Fujikawa. In 1983, Alvarez-Gaum\\'e and Witten observed that one can simplify this evaluation by replacing the operators which appear in the regulator and in the jacobian by quantum mechanical operators with the same (anti)commutation relations. By rewriting this quantum mechanical trace as a path integral with periodic boundary conditions for a one-dimensional supersymmetric nonlinear sigma model, they obtained the chiral anomalies for spin 1/2 and 3/2 fields and selfdual antisymmetric tensors in d dimensions. In this article, we treat the case of trace anomalies for spin 0, 1/2 and 1 fields in a gravitational and Yang-Mills background. We do not introduce a supersymmetric sigma model, but keep the original Dirac matrices $\\g^\\m$ and internal symmetry generators $T^a$ in the path integral. As a result, we get a matrix-valued action. Gauge covariance o...
The Linguistic Interpretation of Quantum Mechanics
Ishikawa, Shiro
2012-01-01
About twenty years ago, we proposed the mathematical formulation of Heisenberg's uncertainty principle, and further, we concluded that Heisenberg's uncertainty principle and EPR-paradox are not contradictory. This is true, however we now think that we should have argued about it under a certain firm interpretation of quantum mechanics. Recently we proposed the linguistic quantum interpretation (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy). In fact, we can consider that traditional philosophies have progressed toward quantum philosophy. In this paper, we first review the linguistic quantum interpretation, and further, clarify the relation between EPR-paradox and Heisenberg's uncertainty...
Negative entropy and information in quantum mechanics
Cerf, N. J.; Adami, C.
1995-01-01
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon) information theory, quantum (von Neumann) conditional entropies can be negative when considering quantum entangled systems, a fact related to quantum non-separability. The possibility that negative (virtual) information can be carried by entangled particles sug...
Teaching Quantum Mechanics on an Introductory Level.
Muller, Rainer; Wiesner, Hartmut
2002-01-01
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
Teaching Quantum Mechanics on an Introductory Level.
Muller, Rainer; Wiesner, Hartmut
2002-01-01
Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)
Hidden scale in quantum mechanics
Giri, Pulak Ranjan
2007-01-01
We show that the intriguing localization of a free particle wave-packet is possible due to a hidden scale present in the system. Self-adjoint extensions (SAE) is responsible for introducing this scale in quantum mechanical models through the nontrivial boundary conditions. We discuss a couple of classically scale invariant free particle systems to illustrate the issue. In this context it has been shown that a free quantum particle moving on a full line may have localized wave-packet around the origin. As a generalization, it has also been shown that particles moving on a portion of a plane or on a portion of a three dimensional space can have unusual localized wave-packet.
Quantum mechanics: Myths and facts
Nikolic, H
2006-01-01
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
Matrix Quantum Mechanics from Qubits
Hartnoll, Sean A; Mazenc, Edward A
2016-01-01
We introduce a transverse field Ising model with order N^2 spins interacting via a nonlocal quartic interaction. The model has an O(N,Z), hyperoctahedral, symmetry. We show that the large N partition function admits a saddle point in which the symmetry is enhanced to O(N). We further demonstrate that this `matrix saddle' correctly computes large N observables at weak and strong coupling. The matrix saddle undergoes a continuous quantum phase transition at intermediate couplings. At the transition the matrix eigenvalue distribution becomes disconnected. The critical excitations are described by large N matrix quantum mechanics. At the critical point, the low energy excitations are waves propagating in an emergent 1+1 dimensional spacetime.
Quantum Mechanics: Myths and Facts
Nikolić, Hrvoje
2007-11-01
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
Deformation of noncommutative quantum mechanics
Jiang, Jian-Jian; Chowdhury, S. Hasibul Hassan
2016-09-01
In this paper, the Lie group GNC α , β , γ , of which the kinematical symmetry group GNC of noncommutative quantum mechanics (NCQM) is a special case due to fixed nonzero α, β, and γ, is three-parameter deformation quantized using the method suggested by Ballesteros and Musso [J. Phys. A: Math. Theor. 46, 195203 (2013)]. A certain family of QUE algebras, corresponding to GNC α , β , γ with two of the deformation parameters approaching zero, is found to be in agreement with the existing results of the literature on quantum Heisenberg group. Finally, we dualize the underlying QUE algebra to obtain an expression for the underlying star-product between smooth functions on GNC α , β , γ .
A quantum mechanical model of "dark matter"
Belokurov, V V
2014-01-01
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
Quantum Jacobi fields in Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Entropy, Topological Theories and Emergent Quantum Mechanics
Directory of Open Access Journals (Sweden)
D. Cabrera
2017-02-01
Full Text Available The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a ﬁnite dimensional Hilbert space of quantum states. Speciﬁcally, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological ﬁeld theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.
Fun with supersymmetric quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Freedman, B.; Cooper, F.
1984-04-01
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup ..cap alpha../ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index ..delta.. which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if ..delta.. is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate ..delta.. for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references.
Correspondence Truth and Quantum Mechanics
Karakostas, Vassilios
2015-01-01
The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either 'true' or 'false', describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of 'no go' theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton 'uniqueness theorem' is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state...
Transfer of Learning in Quantum Mechanics
Singh, Chandralekha
2016-01-01
We investigate the difficulties that undergraduate students in quantum mechanics courses have in transferring learning from previous courses or within the same course from one context to another by administering written tests and conducting individual interviews. Quantum mechanics is abstract and its paradigm is very different from the classical one. A good grasp of the principles of quantum mechanics requires creating and organizing a knowledge structure consistent with the quantum postulates. Previously learned concepts such as the principle of superposition and probability can be useful in quantum mechanics if students are given opportunity to build associations between new and prior knowledge. We also discuss the need for better alignment between quantum mechanics and modern physics courses taken previously because semi-classical models can impede internalization of the quantum paradigm in more advanced courses.
Quantum localization of Classical Mechanics
Batalin, Igor A
2016-01-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Quantum localization of classical mechanics
Batalin, Igor A.; Lavrov, Peter M.
2016-07-01
Quantum localization of classical mechanics within the BRST-BFV and BV (or field-antifield) quantization methods are studied. It is shown that a special choice of gauge fixing functions (or BRST-BFV charge) together with the unitary limit leads to Hamiltonian localization in the path integral of the BRST-BFV formalism. In turn, we find that a special choice of gauge fixing functions being proportional to extremals of an initial non-degenerate classical action together with a very special solution of the classical master equation result in Lagrangian localization in the partition function of the BV formalism.
Supersymmetric Quantum Mechanics and Topology
Directory of Open Access Journals (Sweden)
Muhammad Abdul Wasay
2016-01-01
Full Text Available Supersymmetric quantum mechanical models are computed by the path integral approach. In the β→0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold.
Quantum mechanics in phase space
DEFF Research Database (Denmark)
Hansen, Frank
1984-01-01
A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...
Path integration in relativistic quantum mechanics
Redmount, I H; Redmount, Ian H.; Suen, Wai-Mo
1993-01-01
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.
Quantum mechanics for applied physics and engineering
Fromhold, Albert T
2011-01-01
This excellent text, directed to upper-level undergraduates and graduate students in engineering and applied physics, introduces the fundamentals of quantum mechanics, emphasizing those aspects of quantum mechanics and quantum statistics essential to an understanding of solid-state theory. A heavy background in mathematics and physics is not required beyond basic courses in calculus, differential equations, and calculus-based elementary physics.The first three chapters introduce quantum mechanics (using the Schrödinger equations), quantum statistics, and the free-electron theory of metals. Ch
A Quantum Space Behind Simple Quantum Mechanics
Chew, Chuan Sheng; Payne, Jason
2016-01-01
In physics, we are supposed to learn from experiments what constitutes a good/correct theoretical/mathematical model of any physical concept, the physical space should not be an exception. The best picture of the physical space, in Newtonian physics, is given by the configuration space of a free particle. The space, as well as the phase space, can be constructed as a representation space of the relativity symmetry. Starting with the corresponding quantum symmetry, we illustrate the construction of a quantum space along the lines of the quantum phase space and demonstrate the retrieval of the classical picture as an approximation through the contraction of the (relativity) symmetry and the representations of it. The result suggests a picture of the physical space beyond that of a finite dimensional manifold.
The emerging quantum the physics behind quantum mechanics
Pena, Luis de la; Valdes-Hernandez, Andrea
2014-01-01
This monograph presents the latest findings from a long-term research project intended to identify the physics behind Quantum Mechanics. A fundamental theory for quantum mechanics is constructed from first physical principles, revealing quantization as an emergent phenomenon arising from a deeper stochastic process. As such, it offers the vibrant community working on the foundations of quantum mechanics an alternative contribution open to discussion. The book starts with a critical summary of the main conceptual problems that still beset quantum mechanics. The basic consideration is then introduced that any material system is an open system in permanent contact with the random zero-point radiation field, with which it may reach a state of equilibrium. Working from this basis, a comprehensive and self-consistent theoretical framework is then developed. The pillars of the quantum-mechanical formalism are derived, as well as the radiative corrections of nonrelativistic QED, while revealing the underlying physi...
Potentiality, Actuality, and Quantum Mechanics
Directory of Open Access Journals (Sweden)
Boris Koznjak
2007-12-01
Full Text Available In this paper a possible interpretative value of Aristotle’s fundamental ontological doctrine of potentiality (δύναµις and actuality (ἐνέργεια is considered in the context of operationally undoubtedly the most successful but interpretatively still controversial theory of modern physics – quantum mechanics – especially regarding understanding the nature of the world, the phenomena of which it describes and predicts so successfully. In particular, beings of the atomic world are interpreted as real potential beings (δυνάµει ὄντα actualized by the measurement process in appropriate experimental arrangement, and the problem of actual beings (ἐνεργείᾳ ὄντα of the atomic world (better known as the measurement problem in quantum mechanics is considered in the context of Aristotle’s threefold requirement for the priority of actuality over potentiality – in time (χρόνος, definition or knowledge (λόγος, and substantiality (οὐσία.
Bridging classical and quantum mechanics
Haddad, D.; Seifert, F.; Chao, L. S.; Li, S.; Newell, D. B.; Pratt, J. R.; Williams, C.; Schlamminger, S.
2016-10-01
Using a watt balance and a frequency comb, a mass-energy equivalence is derived. The watt balance compares mechanical power measured in terms of the meter, the second, and the kilogram to electrical power measured in terms of the volt and the ohm. A direct link between mechanical action and the Planck constant is established by the practical realization of the electrical units derived from the Josephson and the quantum Hall effects. By using frequency combs to measure velocities and acceleration of gravity, the unit of mass can be realized from a set of three defining constants: the Planck constant h, the speed of light c, and the hyperfine splitting frequency of 133Cs.
Quantum Mechanics of Palladium Nanostructures
Hira, Ajit; McKeough, James; Ortiz, Bridget; Diaz, Juan
We continue our interest in the chemisorption of different atomic and molecular species on small clusters of metallic elements, by examining the interactions of H, H2, Li and O adsorbates with Pdn clusters (n = 2 thru 20). The study of clusters can reveal the effects of substrate geometry on the behavior of adsorbates. Transition-metal clusters are especially suited for the study of quantum size effects and for formation of metallic states, and are ideal candidates for catalytic processes. Hybrid ab initio methods of quantum chemistry (particularly the DFT-B3LYP model) are used to derive optimal geometries for the clusters of interest. We compare calculated binding energies, bond-lengths, ionization potentials, electron affinities and HOMO-LUMO gaps for the clusters. Of particular interest are the comparisons of binding strengths at the three important types of sites: edge (E), hollow (H), on-top (T), threefold sites and fourfold sites. Effects of crystal symmetries corresponding to the bulk structures are investigated. The capacity of Pd clusters to adsorb H atoms will be compared to Ni clusters. Admixture with Pt atoms will also be considered.
Emergent quantum mechanics and emergent symmetries
Hooft, G. 't
2007-01-01
Quantum mechanics is ‘emergent’ if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present in the underlying deterministic system. Such
A Process Model of Quantum Mechanics
Sulis, William
2014-01-01
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise through a non-uniform interpolation process. Standard non-relativistic quantum mechanics emerges under the limit of infinite information (the causal space grows to infinity) and infinitesimal scale (the separation between points goes to zero). The model has th...
Quantum plasmonics: from jellium models to ab initio calculations
Directory of Open Access Journals (Sweden)
Varas Alejandro
2016-08-01
Full Text Available Light-matter interaction in plasmonic nanostructures is often treated within the realm of classical optics. However, recent experimental findings show the need to go beyond the classical models to explain and predict the plasmonic response at the nanoscale. A prototypical system is a nanoparticle dimer, extensively studied using both classical and quantum prescriptions. However, only very recently, fully ab initio time-dependent density functional theory (TDDFT calculations of the optical response of these dimers have been carried out. Here, we review the recent work on the impact of the atomic structure on the optical properties of such systems. We show that TDDFT can be an invaluable tool to simulate the time evolution of plasmonic modes, providing fundamental understanding into the underlying microscopical mechanisms.
Energy Technology Data Exchange (ETDEWEB)
Whitaker, A [Department of Physics, Queen' s University, Belfast (United Kingdom)
2004-02-27
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. To commence with general discussion of the new book, the authors recognise that the graduate student of today almost certainly has substantial experience of wave mechanics, and is probably familiar with the Dirac formalism. The new edition has been almost entirely rewritten; even at the level of basic text, it is difficult to trace sentences or paragraphs that have moved unscathed from one edition to the next. As well as the new topics, many of the old ones are discussed in much greater depth, and the general organisation is entirely different. As compared with the steady rise in level of the 1966 edition, the level of this book is fairly consistent throughout, and from the perspective of a beginning graduate student, I would estimate, a little tough. To sum up, Gottfried and Yan's book contains a vast amount of knowledge and understanding
Schwinger Algebra for Quaternionic Quantum Mechanics
Horwitz, L P
1997-01-01
It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states $N \\to \\infty$.
Bohmian mechanics and the quantum revolution
Goldstein, S
1995-01-01
This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics'' by John Bell and ``The Undivided Universe: An Ontological Interpretation of Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors concerning the character of quantum theory and quantum reality---and, in particular, their approaches to the issues of nonlocality, the possibility of hidden variables, and the nature of and desiderata for a satisfactory scientific explanation of quantum phenomena---are contrasted, with each other and with the orthodox approach to these issues.
Quantum mechanics and computation; Quanta y Computacion
Energy Technology Data Exchange (ETDEWEB)
Cirac Sasturain, J. I.
2000-07-01
We review how some of the basic principles of Quantum Mechanics can be used in the field of computation. In particular, we explain why a quantum computer can perform certain tasks in a much more efficient way than the computers we have available nowadays. We give the requirements for a quantum system to be able to implement a quantum computer and illustrate these requirements in some particular physical situations. (Author) 16 refs.
Interactive learning tutorials on quantum mechanics
Singh, Chandralekha
2016-01-01
We discuss the development and evaluation of quantum interactive learning tutorials (QuILTs) which are suitable for undergraduate courses in quantum mechanics. QuILTs are based on the investigation of student difficulties in learning quantum physics. They exploit computer-based visualization tools and help students build links between the formal and conceptual aspects of quantum physics without compromising the technical content. They can be used both as supplements to lectures or as a self-study tool.
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Oss, Stefano; Rosi, Tommaso
2015-04-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.
Towards a Constructive Foundation of Quantum Mechanics
Smilga, Walter
2016-11-01
I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space-time has a discrete spectrum, relative to classical observers in space-time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.
Towards a Constructive Foundation of Quantum Mechanics
Smilga, Walter
2017-01-01
I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space-time has a discrete spectrum, relative to classical observers in space-time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.
Quantum Mechanics As A Limiting Case of Classical Mechanics
Ghose, Partha
2000-01-01
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which quantum mechanics emerges as a limiting case of classical mechanics in which the classical system is decoupled from its environment.
Quantum chemical calculations of glycine glutaric acid
Arioǧlu, ćaǧla; Tamer, Ömer; Avci, Davut; Atalay, Yusuf
2017-02-01
Density functional theory (DFT) calculations of glycine glutaric acid were performed by using B3LYP levels with 6-311++G(d,p) basis set. The theoretical structural parameters such as bond lengths and bond angles are in a good agreement with the experimental values of the title compound. HOMO and LUMO energies were calculated, and the obtained energy gap shows that charge transfer occurs in the title compound. Vibrational frequencies were calculated and compare with experimental ones. 3D molecular surfaces of the title compound were simulated using the same level and basis set. Finally, the 13C and 1H NMR chemical shift values were calculated by the application of the gauge independent atomic orbital (GIAO) method.
Quantum mechanics without potential function
Energy Technology Data Exchange (ETDEWEB)
Alhaidari, A. D., E-mail: haidari@sctp.org.sa [Saudi Center for Theoretical Physics, P.O. Box 32741, Jeddah 21438 (Saudi Arabia); Ismail, M. E. H. [Department of Mathematics, University of Central Florida, Orlando, Florida 32816 (United States)
2015-07-15
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrödinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.
Quantum mechanics of Proca fields
Zamani, Farhad; Mostafazadeh, Ali
2009-05-01
We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries.
A modern approach to quantum mechanics
Townsend, John S
2012-01-01
Using an innovative approach that students find both accessible and exciting, A Modern Approach to Quantum Mechanics, Second Edition lays out the foundations of quantum mechanics through the physics of intrinsic spin. Written to serve as the primary textbook for an upper-division course in quantum mechanics, Townsend's text gives professors and students a refreshing alternative to the old style of teaching, by allowing the basic physics of spin systems to drive the introduction of concepts such as Dirac notation, operators, eigenstates and eigenvalues, time evolution in quantum mechanics, and entanglement. Chapters 6 through 10 cover the more traditional subjects in wave mechanics-the Schrodinger equation in position space, the harmonic oscillator, orbital angular momentum, and central potentials-but they are motivated by the foundations developed in the earlier chapters. Students using this text will perceive wave mechanics as an important aspect of quantum mechanics, but not necessarily the core of the subj...
Quantum Mechanics: Bell and Quantum Entropy for the Classroom
Pluch, Philipp
2014-01-01
In this article we are willing to give some first steps to quantum mechanics and a motivation of quantum mechanics and its interpretation for undergraduate students not from physics. After a short historical review in the development we discuss philosophical, physical and mathematical interpretation. We define local realism, locality and hidden variable theory which ends up in the EPR paradox, a place where questions on completeness and reality comes into play. The fundamental result of the last century was maybe Bell's that states that local realism is false if quantum mechanics is true. From this fact we can obtain the so called Bell inequalities. After a didactic example of the fact what these inequalities means we describe the key concept of quantum entanglement motivated here by quantum information theory. Also classical entropy and von Neuman entropy is discussed.
Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology
Gell-Mann, Murray; Gell-Mann, Murray; Hartle, James B.
1993-01-01
We investigate the origin of the arrow of time in quantum mechanics in the context of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured subsystems incorporates a fundamental arrow of time. Extending discussions of Aharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a generalized quantum mechanics for cosmology that utilizes both an initial and a final density matrix to give a time-neutral formulation without a fundamental arrow of time. Time asymmetries can arise for particular universes from differences between their initial and final conditions. Theories for both would be a goal of quantum cosmology. A special initial condition and a final condition of indifference would be sufficient to explain the observed time asymmetries of the universe. In this essay we ask under what circumstances a completely time symmetric universe, with T-symmetric initial and final condition, could be consistent with the time asymmetries of the limited domain of our experience. We discuss the ap...
Frka, Sanja; Šala, Martin; Kroflič, Ana; Huš, Matej; Čusak, Alen; Grgić, Irena
2016-06-01
Methylnitrocatechols (MNCs) are secondary organic aerosol (SOA) tracers and major contributors to atmospheric brown carbon; however, their formation and aging processes in atmospheric waters are unknown. To investigate the importance of aqueous-phase electrophilic substitution of 3-methylcatechol with nitronium ion (NO2(+)), we performed quantum calculations of their favorable pathways. The calculations predicted the formation of 3-methyl-5-nitrocatechol (3M5NC), 3-methyl-4-nitrocatechol (3M4NC), and a negligible amount of 3-methyl-6-nitrocatechol (3M6NC). MNCs in atmospheric PM2 samples were further inspected by LC/(-)ESI-MS/MS using commercial as well as de novo synthesized authentic standards. We detected 3M5NC and, for the first time, 3M4NC. In contrast to previous reports, 3M6NC was not observed. Agreement between calculated and observed 3M5NC/3M4NC ratios cannot unambiguously confirm the electrophilic mechanism as the exclusive formation pathway of MNCs in aerosol water. However, the examined nitration by NO2(+) is supported by (1) the absence of 3M6NC in the ambient aerosols analyzed and (2) the constant 3M5NC/3M4NC ratio in field aerosol samples, which indicates their common formation pathway. The magnitude of error one could make by incorrectly identifying 3M4NC as 3M6NC in ambient aerosols was also assessed, suggesting the importance of evaluating the literature regarding MNCs with special care.
Pragmatic Information in Quantum Mechanics
Roederer, Juan G
2015-01-01
An objective definition of pragmatic information and the consideration of recent results about information processing in the human brain can help overcome some traditional difficulties with the interpretation of quantum mechanics. Rather than attempting to define information ab initio, I introduce the concept of interaction between material bodies as a primary concept. Two distinct categories can be identified: 1) Interactions which can always be reduced to a superposition of physical interactions (forces) between elementary constituents; 2) Interactions between complex bodies which cannot be reduced to a superposition of interactions between parts, and in which patterns and forms (in space and/or time) play the determining role. Pragmatic information is then defined as the correspondence between a given pattern and the ensuing pattern-specific change. I will show that pragmatic information is a biological concept that plays no active role in the purely physical domain; it only does so when a living organism ...
Morlet Wavelets in Quantum Mechanics
Directory of Open Access Journals (Sweden)
John Ashmead
2012-11-01
Full Text Available Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the use of plane wave or δ function decomposition. Morlet wavelets in particular are well-suited for this work: as Gaussians, they have a simple analytic form and they work well with Feynman path integrals. But to take full advantage of Morlet wavelets we need to supply an explicit form for the inverse Morlet transform and a manifestly covariant form for the four-dimensional Morlet wavelet. We construct both here.Quanta 2012; 1: 58–70.
Kindergarten Quantum Mechanics lectures notes
Coecke, B
2005-01-01
These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes quant-ph/0506132. In a last section we provide some pointers to the body of technical literature on the subject.
Testing non-associative quantum mechanics
Bojowald, Martin; Buyukcam, Umut
2015-01-01
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to non-associative algebras. Their quantum physics has remained obscure. This letter presents the first derivation of potentially testable physical results in non-associative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
Algebraic-statistical approach to quantum mechanics
Slavnov, D A
2001-01-01
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative algebra (observables) and the nonlinear functionals on this algebra (physical states) are used as the primary constituents. The functionals associate with results of a particular measurement. It is suggested to consider certain ensembles of the physical states as quantum states of the standart quantum mechanics. It is shown that in such scheme the mathematical formalism of the standart quantum mechanics can be reproduced completely.
Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics.
Goldfarb, Yair; Degani, Ilan; Tannor, David J
2006-12-21
In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification-a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10(-7) calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity.
Random Matrix theory approach to Quantum mechanics
Chaitanya, K. V. S. Shiv
2015-01-01
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of random matrix theory. This study helps in identify the potential appear in the joint probability distribution function in the random matrix theory as a super potential. This approach allows to extend the random matrix theory to the newly discovered exceptional ...
Vibrational Spectra and Quantum Calculations of Ethylbenzene
Institute of Scientific and Technical Information of China (English)
Jian Wang; Xue-jun Qiu; Yan-mei Wang; Song Zhang; Bing Zhang
2012-01-01
Normal vibrations of ethylbenzene in the first excited state have been studied using resonant two-photon ionization spectroscopy.The band origin of ethylbenzene of S1←S0 transition appeared at 37586 cm-1.A vibrational spectrum of 2000 cm-1 above the band origin in the first excited state has been obtained.Several chain torsions and normal vibrations are obtained in the spectrum.The energies of the first excited state are calculated by the time-dependent density function theory and configuration interaction singles (CIS) methods with various basis sets.The optimized structures and vibrational frequencies of the S0 and S1 states are calculated using Hartree-Fock and CIS methods with 6-311++G(2d,2p) basis set.The calculated geometric structures in the S0 and S1 states are gauche conformations that the symmetric plane of ethyl group is perpendicular to the ring plane.All the observed spectral bands have been successfully assigned with the help of our calculations.
Review of student difficulties in upper-level quantum mechanics
National Research Council Canada - National Science Library
Chandralekha Singh; Emily Marshman
2015-01-01
... at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical mechanics and quantum mechanics are very different...
Elucidating reaction mechanisms on quantum computers.
Reiher, Markus; Wiebe, Nathan; Svore, Krysta M; Wecker, Dave; Troyer, Matthias
2017-07-18
With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.
The transactional interpretation of quantum mechanics
Cramer, John G.
2001-06-01
The transactional interpretation of quantum mechanics [1] was originally published in 1986 and is now about 14 years old. It is an explicitly nonlocal and Lorentz invariant alternative to the Copenhagen interpretation. It interprets the formalism for a quantum interaction as describing a "handshake" between retarded waves (ψ) and advanced waves (ψ*) for each quantum event or "transaction" in which energy, momentum, angular momentum, and other conserved quantities are transferred. The transactional interpretation offers the advantages that (1) it is actually "visible" in the formalism of quantum mechanics, (2) it is economical, involving fewer independent assumptions than its rivals, (3) it is paradox-free, resolving all of the paradoxes of standard quantum theory including nonlocality and wave function collapse, (4) it does not give a privileged role to observers or measurements, and (5) it permits the visualization of quantum events. We will review the transactional interpretation and some of its applications to "quantum paradoxes."
Jiménez-Osés, Gonzalo; García, José I; Corzana, Francisco; Elguero, José
2011-05-20
A new protocol combining classical MD simulations and DFT calculations is presented to accurately estimate the (1)H NMR chemical shifts of highly mobile guest-host systems and their thermal dependence. This strategy has been successfully applied for the hydrogen molecule trapped into C(60) fullerene, an unresolved and challenging prototypical case for which experimental values have never been reproduced. The dependence of the final values on the theoretical method and their implications to avoid over interpretation of the obtained results are carefully described.
Critique of Conventional Relativistic Quantum Mechanics.
Fanchi, John R.
1981-01-01
Following an historical sketch of the development of relativistic quantum mechanics, a discussion of the still unresolved difficulties of the currently accepted theories is presented. This review is designed to complement and update the discussion of relativistic quantum mechanics presented in many texts used in college physics courses. (Author/SK)
DEFF Research Database (Denmark)
van Harrevelt, Rob; Honkala, Johanna Karoliina; Nørskov, Jens Kehlet
2005-01-01
Quantum-mechanical calculations of the reaction rate for dissociative adsorption of N-2 on stepped Ru(0001) are presented. Converged six-dimensional quantum calculations for this heavy-atom reaction have been performed using the multiconfiguration time-dependent Hartree method. A potential...
On the Classical Limit of Quantum Mechanics
Allori, V; Allori, Valia; Zangh\\`{\\i}, Nino
2001-01-01
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the $\\h \\to 0$ asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing real objects in an observer-independent way.
Energy Technology Data Exchange (ETDEWEB)
Guimaraes, F.B.
2002-03-07
In this work we describe neutron and proton induced reaction cross-sections for iron produced by the codes TNG and CEM95 in the 5 to 300 MeV energy range. TNG calculations cover the 5-90 MeV range, while CEM95 covers the 50-300 MeV high energy range. The two codes show some disagreements in the overlap energy range, both among themselves and with the experimental data, which are presently being addressed. The experimental data used are from NNDC and/or from LA150 NSE references. We also describe some developments for combining TNG and CEM95 into a new code called CETNG (Cascade Exciton TNG).
Directory of Open Access Journals (Sweden)
Humberto J. Domínguez
2014-01-01
Full Text Available Marine organisms are an increasingly important source of novel metabolites, some of which have already inspired or become new drugs. In addition, many of these molecules show a high degree of novelty from a structural and/or pharmacological point of view. Structure determination is generally achieved by the use of a variety of spectroscopic methods, among which NMR (nuclear magnetic resonance plays a major role and determination of the stereochemical relationships within every new molecule is generally the most challenging part in structural determination. In this communication, we have chosen okadaic acid as a model compound to perform a computational chemistry study to predict 1H and 13C NMR chemical shifts. The effect of two different solvents and conformation on the ability of DFT (density functional theory calculations to predict the correct stereoisomer has been studied.
Conference on Mathematical Results in Quantum Mechanics
Exner, Pavel; Tater, Miloš; QMath-7
1999-01-01
At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.
Propagators in Polymer Quantum Mechanics
Flores-González, Ernesto; Reyes, Juan D
2013-01-01
Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has been used to represent some aspects of the loop quantization in a simpler context, and, on the other, it has been applied to each of the infinite mechanical modes of other systems. Indeed, this polymer approach was recently implemented for the free scalar field propagator. In this work we compute the polymer propagators of the free particle and a particle in a box; amusingly, just as in the non polymeric case, the one of the particle in a box may be computed also from that of the free particle using the method of images. We verify the propagators hereby obtained satisfy standard properties such as: consistency with initial conditions, composition and Green's function character. Furthermore they are also shown to reduce to the usual Schr\\"odinger propagators in the limit of sm...
Quantum Semiotics: A Sign Language for Quantum Mechanics
Prashant
2006-01-01
Semiotics is the language of signs which has been used effectively in various disciplines of human scientific endeavor. It gives a beautiful and rich structure of language to express the basic tenets of any scientific discipline. In this article we attempt to develop from first principles such an axiomatic structure of semiotics for Quantum Mechanics. This would be a further enrichment to the already existing well understood mathematical structure of Quantum Mechanics but may give new insights and understanding to the theory and may help understand more lucidly the fundamentality of Nature which Quantum Theory attempts to explain.
A quantum mechanical study of alkylimidazolium halide ionic liquids
Li, Wei; Qi, Chuansong; Rong, Hua; Wu, Xinmin; Gong, Liangfa
2012-07-01
Thirty imidazolium (IM) halide compounds were studied using quantum chemical calculations. Geometry optimization and interaction energy calculations were performed using the B3LYP/6-311++G(d,p) method for ions composed of one alkylimidazolium cation and two or three halogen anions. The obtained structures were consistent with experimental results. In addition, a linear correlation between melting points and interaction energies was obtained for the compounds studied, and this relationship was consistent with that obtained for amino acid cation based ionic liquids. Our Letter demonstrates the potential for quantum mechanical calculations to predict the melting points of ionic liquids.
Reactivity of Tourmaline by Quantum Chemical Calculations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
ZnAb initio calculations on reactivity of tourmaline were performed using both Gaussian and density function theory discrete variation method (DFT-DVM). The HF, B3LYP methods and basis sets STO-3G(3d,3p),6-31G(3d,3p) and 6-311++G(3df,3pd) were used in the calculations. The experimental results show energy value obtained from B3LYP and 6-31++1G(3df,3pd) basis sets is more accurate than those from other methods. The highest occupied molecular orbital (HOMO) of the tourmaline cluster mainly consists of O atom of hydroxyl group with relative higher energy level, suggesting that chemical bond between those of electron acceptor and this site may readily form, indicating the higher reactivity of hydroxyl group. The lowest unoccupied molecular orbital (LUMO) of the tourmaline cluster are dominantly composed of Si, O of tetrahedron and Na with relative lower energy level, suggesting that these atoms may tend to form chemical bond with those of electron donor. The results also prove that the O atoms of the tourmaline cluster have stronger reactivity than other atoms.
Dorit Aharonov; Umesh Vazirani
2012-01-01
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity. We describe how QM can be tested in this regime by extending the usual scientific paradigm to include {\\it interactive experiments}.
Bibliographic guide to the foundations of quantum mechanics and quantum information
Cabello, A
2000-01-01
This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation.
Prologue to super quantum mechanics something is rotten in the state of quantum mechanics
Vaguine, Victor
2012-01-01
Since its foundation more than eight decades ago, quantum mechanics has been plagued by enigmas, mysteries and paradoxes and held hostage by quantum positivism. This fact strongly suggests that something is fundamentally wrong with the quantum mechanics paradigm. The best scientific minds, such as Albert Einstein, Louis de Broglie, David Bohm, Richard Feynman and others have spent years of their professional lives attempting to find resolution to the quantum mechanics predicament, with not much success. A shift of the quantum mechanics paradigm toward a deeper physics theory is long overdue.
Topological strings from quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Grassi, Alba; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematique; Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2014-12-15
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P{sup 2}, local P{sup 1} x P{sup 1} and local F{sub 1}. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.
Topological Strings from Quantum Mechanics
Grassi, Alba; Marino, Marcos
2014-01-01
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized theta function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P2, local P1xP1 and local F1. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Phys...
Strange Bedfellows: Quantum Mechanics and Data Mining
Energy Technology Data Exchange (ETDEWEB)
Weinstein, Marvin [SLAC National Accelerator Laboratory, Stanford, CA (United States)
2010-02-15
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
On the tomographic picture of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ibort, A., E-mail: albertoi@math.uc3m.e [Departamento de Matematicas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganes, Madrid (Spain); Man' ko, V.I., E-mail: manko@na.infn.i [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, G., E-mail: marmo@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Simoni, A., E-mail: simoni@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy); Ventriglia, F., E-mail: ventriglia@na.infn.i [Dipartimento di Scienze Fisiche dell' Universita ' Federico II' e Sezione INFN di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126 Naples (Italy)
2010-06-07
We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by means of Naimark positive definite functions on the Weyl-Heisenberg group. This connection is used to formulate properties which guarantee that tomographic probabilities describe quantum states in the probability representation of quantum mechanics.
Strange Bedfellows: Quantum Mechanics and Data Mining
Energy Technology Data Exchange (ETDEWEB)
Weinstein, Marvin; /SLAC
2009-12-16
Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.
Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries.
Sun, Qiming; Chan, Garnet Kin-Lic
2014-09-09
Motivated by recent work in density matrix embedding theory, we define exact link orbitals that capture all quantum mechanical (QM) effects across arbitrary quantum mechanics/molecular mechanics (QM/MM) boundaries. Exact link orbitals are rigorously defined from the full QM solution, and their number is equal to the number of orbitals in the primary QM region. Truncating the exact set yields a smaller set of link orbitals optimal with respect to reproducing the primary region density matrix. We use the optimal link orbitals to obtain insight into the limits of QM/MM boundary treatments. We further analyze the popular general hybrid orbital (GHO) QM/MM boundary across a test suite of molecules. We find that GHOs are often good proxies for the most important optimal link orbital, although there is little detailed correlation between the detailed GHO composition and optimal link orbital valence weights. The optimal theory shows that anions and cations cannot be described by a single link orbital. However, expanding to include the second most important optimal link orbital in the boundary recovers an accurate description. The second optimal link orbital takes the chemically intuitive form of a donor or acceptor orbital for charge redistribution, suggesting that optimal link orbitals can be used as interpretative tools for electron transfer. We further find that two optimal link orbitals are also sufficient for boundaries that cut across double bonds. Finally, we suggest how to construct "approximately" optimal link orbitals for practical QM/MM calculations.
SPECTRAL CALCULATIONS OF HAMILTONIAN FOR A QUANTUM FRACTAL NETWORK
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A general formulation for the spectral calculations of the Hamiltonian operator of a Quantum Fractal Network(QFN) is presented. The QFN can be constructed by placing artificial neurons on each site of the fractal lattice. An artificial neuron may consist of a cell of a quantum cellular automaton or a quantum dot, which confines a single electron. The Coulomb interaction or the spin-spin interaction between neurons can be used to transmit signals and perform logic operations.The recursive formulas of the eigenvalues and eigenvectors between sub-lattices are obtained explicitly. As the application of the formulations,the eigenvalues and eigenvectors of the Hamiltonian operator for the Sierpinski gasket are calculated.
The Interpretation of Quantum Mechanics Many Worlds or Many Words?
Tegmark, M
1998-01-01
As cutting-edge experiments display ever more extreme forms of non-classical behavior, the prevailing view on the interpretation of quantum mechanics appears to be gradually changing. A (highly unscientific) poll taken at the 1997 UMBC quantum mechanics workshop gave the once all-dominant Copenhagen interpretation less than half of the votes. The Many Worlds interpretation (MWI) scored second, comfortably ahead of the Consistent Histories and Bohm interpretations. It is argued that since all the above-mentioned approaches to nonrelativistic quantum mechanics give identical cookbook prescriptions for how to calculate things in practice, practical-minded experimentalists, who have traditionally adopted the ``shut-up-and-calculate interpretation'', typically show little interest in whether cozy classical concepts are in fact real in some untestable metaphysical sense or merely the way we subjectively perceive a mathematically simpler world where the Schrodinger equation describes everything - and that they are t...
A New Interpretation to The Quantum Mechanics
Feng, Yulei
2012-01-01
In this paper, we try to give a new interpretation to the quantum mechanics from the point of view of (non-relativistic) quantum field theory. After field quantization, we obtain the Heisenberg equations for the momentum and coordinate operators of the particles excited from the (Schrodinger) field. We then give the probability concepts of quantum mechanics on the base of a statistical assemble realizing the assemble interpretation. With these, we make a series of conceptual modifications to the standard quantum mechanics, especially the quantum measurement theory; in the end, we try to solve the EPR paradox with the use of our new ideas. In addition, we also give a field theoretical description to the double-slit interference experiment, obtaining the particle number distribution, in the appendix.
A new introductory quantum mechanics curriculum
Kohnle, Antje; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth
2013-01-01
The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of interpretive aspects of quantum mechanics and quantum information theory. This article gives an overview of the resources available at the IOP website. The core text is presented as around 80 articles co-authored by leading experts that are arranged in themes and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is part of the resource. Solutions to activities are available ...
Realism and Objectivism in Quantum Mechanics
Karakostas, Vassilios
2012-01-01
The present study attempts to provide a consistent and coherent account of what the world could be like, given the conceptual framework and results of contemporary quantum theory. It is suggested that standard quantum mechanics can, and indeed should, be understood as a realist theory within its domain of application. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional philosophical presuppositions. It is argued, in this direction, that the conceptualization of the nature of reality, as arising out of our most basic physical theory, calls for a kind of contextual realism. Within the domain of quantum mechanics, knowledge of 'reality in itself', 'the real such as it truly is' independent of the way it is contextualized, is impossible in principle. In this connection, the meaning of objectivity in quantum mechanics is analyzed, whilst the important question concerning t...
Quantum ballistic evolution in quantum mechanics application to quantum computers
Benioff, P
1996-01-01
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e. motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also pr...
On some hydrodynamical aspects of quantum mechanics
Spera, Mauro
2009-01-01
In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the Borel-Weil contruction of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dimensional geometric quantum mechanics, the Schr\\"odinger velocity field on projective Hilbert space is divergence-free (being Killing with respect to the Fubini-Study metric) and fulfils the stationary Euler equation, with pressure proportional to the Hamiltonian uncertainty (squared). We explicitly compute the pressure gradient of this "Schr\\"odinger fluid" and determine its critical points. Its vorticity is also calculated and shown to depend on the spacings of the energy levels. These results follow from hydrodynamical properties of Killing vector fields valid in any (finite dimensional) Riemannian manifold, of possible independent interest.
Quantum mechanics in an evolving Hilbert space
Artacho, Emilio
2016-01-01
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalisation, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fibre bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge imp...
Waveform information from quantum mechanical entropy
Funkhouser, Scott; Suski, William; Winn, Andrew
2016-06-01
Although the entropy of a given signal-type waveform is technically zero, it is nonetheless desirable to use entropic measures to quantify the associated information. Several such prescriptions have been advanced in the literature but none are generally successful. Here, we report that the Fourier-conjugated `total entropy' associated with quantum-mechanical probabilistic amplitude functions (PAFs) is a meaningful measure of information in non-probabilistic real waveforms, with either the waveform itself or its (normalized) analytic representation acting in the role of the PAF. Detailed numerical calculations are presented for both adaptations, showing the expected informatic behaviours in a variety of rudimentary scenarios. Particularly noteworthy are the sensitivity to the degree of randomness in a sequence of pulses and potential for detection of weak signals.
Quantum Mechanics Fundamentals and Applications to Technology
Singh, Jasprit
1996-01-01
Explore the relationship between quantum mechanics and information-age applications. This volume takes an altogether unique approach to quantum mechanics. Providing an in-depth exposition of quantum mechanics fundamentals, it shows how these concepts are applied to most of today's information technologies, whether they are electronic devices or materials. No other text makes this critical, essential leap from theory to real-world applications. The book's lively discussion of the mathematics involved fits right in with contemporary multidisciplinary trends in education: Once the basic formulati
A condensed course of quantum mechanics
Cejnar, Pavel
2013-01-01
This book represents a concise summary of non-relativistic quantum mechanics on the level suitable for university students of physics. It covers, perhaps even slightly exceeds, a one-year course of about 50 lectures, requiring basic knowledge of calculus, algebra, classical mechanics and a bit of motivation for the quantum adventure.The exposition is succinct, with minimal narration, but witha maximum of explicit and hierarchically structured mathematical derivations. The text covers all essential topics of university courses of quantum mechanics - from general mathematical formalism to specif
Optimization of a relativistic quantum mechanical engine
Peña, Francisco J.; Ferré, Michel; Orellana, P. A.; Rojas, René G.; Vargas, P.
2016-08-01
We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.
Theoretical and quantum mechanics fundamentals for chemists
Ivanov, Stefan
2006-01-01
Provides the basics of theoretical and quantum mechanics in one place and emphasizes the continuity between themUniquely presented to be used for self-taught courses covering theoretical and quantum mechanicsEach chapter includes a detailed outline, a summary, self-assessment questions for which answers can be found in the textInvaluable for chemistry undergraduate and graduate students, chemists, other non-physical scientists, engineering students of modern techniques and technology, specialists who need a better understanding of quantum mechanics.
Philosophical foundations of interpretations of quantum mechanics
Bezlepkin, Evgeny
2016-01-01
It is demonstrated that the reason for the diversity of interpretations of quantum mechanics is that they are not connected by continuity relations with classical physics, and also the reason is the impossibility of operationalist definition of the vector of state. The problem lies in the incompatibility of the philosophical foundations of interpretations, which results in the difficulty of building a unified picture of the world. To solve the problem, we identify general philosophical foundation of interpretations of quantum mechanics and built their classification. We also show that in more general theories, the part of which is quantum mechanics, it is possible to integrate (reconcile) the philosophical foundations of interpretations.
Efficient wave-function matching approach for quantum transport calculations
DEFF Research Database (Denmark)
Sørensen, Hans Henrik Brandenborg; Hansen, Per Christian; Petersen, Dan Erik;
2009-01-01
The wave-function matching (WFM) technique has recently been developed for the calculation of electronic transport in quantum two-probe systems. In terms of efficiency it is comparable to the widely used Green's function approach. The WFM formalism presented so far requires the evaluation of all ...
Mossbauer neutrinos in quantum mechanics and quantum field theory
Kopp, Joachim
2009-01-01
We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detecti...
Playing Games with Quantum Mechanics
Phoenix, Simon J D
2012-01-01
We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence. We call such games playable. By focusing on the notion of playability for games we can more clearly see the distinction between classical and quantum games and tackle the thorny issue of what it means to quantize a game. The approach we take can more properly be thought of as gaming the quantum rather than quantizing a game and we find that in this perspective we can think of a complete quantum game, for a given set of preferences, as representing a single family of quantum games with many different playable versions. The versions of Quantum Prisoners Dilemma presented in the literature can therefore be thought of specific instances of the single family of Quantum Prisoner's Dilemma with respect to a particular measurement. The conditions for equilibrium are given for playab...
Quantum Mechanics/Molecular Mechanics Study of the Sialyltransferase Reaction Mechanism.
Hamada, Yojiro; Kanematsu, Yusuke; Tachikawa, Masanori
2016-10-11
The sialyltransferase is an enzyme that transfers the sialic acid moiety from cytidine 5'-monophospho-N-acetyl-neuraminic acid (CMP-NeuAc) to the terminal position of glycans. To elucidate the catalytic mechanism of sialyltransferase, we explored the potential energy surface along the sialic acid transfer reaction coordinates by the hybrid quantum mechanics/molecular mechanics method on the basis of the crystal structure of sialyltransferase CstII. Our calculation demonstrated that CstII employed an SN1-like reaction mechanism via the formation of a short-lived oxocarbenium ion intermediate. The computational barrier height was 19.5 kcal/mol, which reasonably corresponded with the experimental reaction rate. We also found that two tyrosine residues (Tyr156 and Tyr162) played a vital role in stabilizing the intermediate and the transition states by quantum mechanical interaction with CMP.
On the principles of quantum mechanics
Sakai, E
2004-01-01
We propose five principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, and probability principle. We deductively establish quantum mechanics on the basis of them. Then we adopt the following four guide lines. First, we do not premise the relations between dynamical variables in classical mechanics. Second, since energy and momentum are quantitatively defined in classical mechanics, we define them in quantum mechanics so that the corresponding conservation laws are satisfied in a coupling system of a quantum particle and a classical particle. Third, we define Planck's constant as a proportionality constant between energy and frequency due to one of Einstein-de Broglie formulas. Fourth, we define mass as a proportionality constant between momentum and velocity. We have succeeded to obtain the canonical commutation relations and the Schroedinger equation for a particle in an external field in the definiti...
Tensor Fields in Relativistic Quantum Mechanics
Dvoeglazov, Valeriy V
2015-01-01
We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We discuss corresponding massless limits. We analize the quantum field theory taking into account the mass dimensions of the notoph and the photon. Next, we deduced the gravitational field equations from relativistic quantum mechanics.
Quantum Mechanics as a Principle Theory
Bub, J
1999-01-01
I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book Interpreting the Quantum World (Cambridge: Cambridge University Press, 1999).
Quantum mechanics as electrodynamics of curvilinear waves
2002-01-01
The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and explains the particularities and the results of the quantum field theory.
Quantum mechanics in simple matrix form
Jordan, Thomas F
1986-01-01
With this text, basic quantum mechanics becomes accessible to undergraduates with no background in mathematics beyond algebra. Containing more than 100 problems, it provides an easy way to learn part of the quantum language and to employ this new skill in solving problems.
Strzalko, Tekla; Wartski, Lya; Corset, Jacques; Castellà-Ventura, Martine; Froment, Françoise
2012-08-01
Mechanisms of alkylation by PhCH(2)Cl or CH(3)I in THF and of deuteriation by DCl (4 N in D(2)O) in THF or THF-toluene of lithiated phenylacetonitrile monoanions and dianions obtained with LHMDS, LDA, or n-BuLi are studied by vibrational and NMR spectroscopy and quantum chemistry calculations. Dialkylation of the three dilithio dianions generated with n-BuLi (2.0-2.7 equiv, THF-hexane) depends on their structure: N-lithio (PhCCNLi)(-)Li(+) and (C,N)-dilithio PhCLiCNLi dianions afford PhCR(2)CN (R = PhCH(2), CH(3)) from the intermediate N-lithio monoalkylated monoanion PhCRCNLi 10; C-lithio dianion (PhCLiCN)(-)Li(+) leads to a carbenoid species, the C-lithio monoalkylated nitrile PhCLiRCN 11, which either eliminates carbene Ph-C-R and different LiCN species or isomerizes to PhCRCNLi in the presence of LiX (X = Cl, I). Dialkylation or dideuteriation of monoanions (monomers, dimers, and heterodimers [PhCHCNLi·LiR'], R' = (SiMe(3))(2)N, (i-Pr)(2)N) obtained with LHMDS or LDA (2.4 equiv, THF) proceeds via a sequential mechanism involving monometalation-monoalkylation (or monodeuteriation) reactions. Some carbene and (LiCNLi)(+) are also observed, and explained by another mechanism implying the C-lithio monoalkylated monoanion PhCLiRCN 9 in the presence of LiX. These results show the ambiphilic behavior of PhCLiRCN as a carbenoid (11) or a carbanion (9) and the importance of LiX formed in situ in the first alkylation step.
Are All Probabilities Fundamentally Quantum Mechanical?
Pradhan, Rajat Kumar
2011-01-01
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated that all probabilities may be fundamentally quantum mechanical in the sense that they may all be derived from the corresponding amplitudes. The classical coin-toss and the quantum double slit interference experiments are discussed as illustrative prototype examples. Absence of multi-order quantum interference effects in multiple-slit experiments and the Experimental tests of complementarity in Wheeler's delayed-choice type experiments are explained using the involvement of the observer.
Quantum mechanical calculations on weakly interacting complexes
Heijmen, T.G.A.
1998-01-01
Symmetry-adapted perturbation theory (SAPT) has been applied to compute the intermolecular potential energy surfaces and the interaction-induced electrical properties of weakly interacting complexes. Asymptotic (large R) expressions have been derived for the contributions to the collision-induced pr
Salazar-Salinas, Karim; Baldera-Aguayo, Pedro A; Encomendero-Risco, Jimy J; Orihuela, Melvin; Sheen, Patricia; Seminario, Jorge M; Zimic, Mirko
2014-08-28
Mycobacterium tuberculosis pyrazinamidase (PZAse) is a key enzyme to activate the pro-drug pyrazinamide (PZA). PZAse is a metalloenzyme that coordinates in vitro different divalent metal cofactors in the metal coordination site (MCS). Several metals including Co(2+), Mn(2+), and Zn(2+) are able to reactivate the metal-depleted PZAse in vitro. We use quantum mechanical calculations to investigate the Zn(2+), Fe(2+), and Mn(2+) metal cofactor effects on the local MCS structure, metal-ligand or metal-residue binding energy, and charge distribution. Results suggest that the major metal-dependent changes occur in the metal-ligand binding energy and charge distribution. Zn(2+) shows the highest binding energy to the ligands (residues). In addition, Zn(2+) and Mn(2+) within the PZAse MCS highly polarize the O-H bond of coordinated water molecules in comparison with Fe(2+). This suggests that the coordination of Zn(2+) or Mn(2+) to the PZAse protein facilitates the deprotonation of coordinated water to generate a nucleophile for catalysis as in carboxypeptidase A. Because metal ion binding is relevant to enzymatic reaction, identification of the metal binding event is important. The infrared vibrational mode shift of the C═Nε (His) bond from the M. tuberculosis MCS is the best IR probe to metal complexation.
Multiscale Quantum Mechanics/Molecular Mechanics Simulations with Neural Networks.
Shen, Lin; Wu, Jingheng; Yang, Weitao
2016-10-11
Molecular dynamics simulation with multiscale quantum mechanics/molecular mechanics (QM/MM) methods is a very powerful tool for understanding the mechanism of chemical and biological processes in solution or enzymes. However, its computational cost can be too high for many biochemical systems because of the large number of ab initio QM calculations. Semiempirical QM/MM simulations have much higher efficiency. Its accuracy can be improved with a correction to reach the ab initio QM/MM level. The computational cost on the ab initio calculation for the correction determines the efficiency. In this paper we developed a neural network method for QM/MM calculation as an extension of the neural-network representation reported by Behler and Parrinello. With this approach, the potential energy of any configuration along the reaction path for a given QM/MM system can be predicted at the ab initio QM/MM level based on the semiempirical QM/MM simulations. We further applied this method to three reactions in water to calculate the free energy changes. The free-energy profile obtained from the semiempirical QM/MM simulation is corrected to the ab initio QM/MM level with the potential energies predicted with the constructed neural network. The results are in excellent accordance with the reference data that are obtained from the ab initio QM/MM molecular dynamics simulation or corrected with direct ab initio QM/MM potential energies. Compared with the correction using direct ab initio QM/MM potential energies, our method shows a speed-up of 1 or 2 orders of magnitude. It demonstrates that the neural network method combined with the semiempirical QM/MM calculation can be an efficient and reliable strategy for chemical reaction simulations.
Babaei, Hassan; Mostafazadeh, Ali
2017-08-01
A first-quantized free photon is a complex massless vector field A =(Aμ ) whose field strength satisfies Maxwell's equations in vacuum. We construct the Hilbert space H of the photon by endowing the vector space of the fields A in the temporal-Coulomb gauge with a positive-definite and relativistically invariant inner product. We give an explicit expression for this inner product, identify the Hamiltonian for the photon with the generator of time translations in H , determine the operators representing the momentum and the helicity of the photon, and introduce a chirality operator whose eigenfunctions correspond to fields having a definite sign of energy. We also construct a position operator for the photon whose components commute with each other and with the chirality and helicity operators. This allows for the construction of the localized states of the photon with a definite sign of energy and helicity. We derive an explicit formula for the latter and compute the corresponding electric and magnetic fields. These turn out to diverge not just at the point where the photon is localized but on a plane containing this point. We identify the axis normal to this plane with an associated symmetry axis and show that each choice of this axis specifies a particular position operator, a corresponding position basis, and a position representation of the quantum mechanics of a photon. In particular, we examine the position wave functions determined by such a position basis, elucidate their relationship with the Riemann-Silberstein and Landau-Peierls wave functions, and give an explicit formula for the probability density of the spatial localization of the photon.
Avoiding Negative Probabilities in Quantum Mechanics
Nyambuya, Golden Gadzirayi
2013-01-01
As currently understood since its discovery, the bare Klein-Gordon theory consists of negative quantum probabilities which are considered to be physically meaningless if not outright obsolete. Despite this annoying setback, these negative probabilities are what led the great Paul Dirac in 1928 to the esoteric discovery of the Dirac Equation. The Dirac Equation led to one of the greatest advances in our understanding of the physical world. In this reading, we ask the seemingly senseless question, "Do negative probabilities exist in quantum mechanics?" In an effort to answer this question, we arrive at the conclusion that depending on the choice one makes of the quantum probability current, one will obtain negative probabilities. We thus propose a new quantum probability current of the Klein-Gordon theory. This quantum probability current leads directly to positive definite quantum probabilities. Because these negative probabilities are in the bare Klein-Gordon theory, intrinsically a result of negative energie...
Superconducting Qubits as Mechanical Quantum Engines
Sachtleben, Kewin; Mazon, Kahio T.; Rego, Luis G. C.
2017-09-01
We propose the equivalence of superconducting qubits with a pistonlike mechanical quantum engine. The work reports a study on the nature of the nonequilibrium work exchanged with the quantum-nonadiabatic working medium, which is modeled as a multilevel coupled quantum well system subject to an external control parameter. The quantum dynamics is solved for arbitrary control protocols. It is shown that the work output has two components: one that depends instantaneously on the level populations and another that is due to the quantum coherences built in the system. The nonadiabatic coherent dynamics of the quantum engine gives rise to a resistance (friction) force that decreases the work output. We consider the functional equivalence of such a device and a rf-SQUID flux qubit.
Progress in post-quantum mechanics
Sarfatti, Jack
2017-05-01
Newton's mechanics in the 17th century increased the lethality of artillery. Thermodynamics in the 19th led to the steam-powered industrial revolution. Maxwell's unification of electricity, magnetism and light gave us electrical power, the telegraph, radio and television. The discovery of quantum mechanics in the 20th century by Planck, Bohr, Einstein, Schrodinger, Heisenberg led to the creation of the atomic and hydrogen bombs as well as computer chips, the world-wide-web and Silicon Valley's multibillion dollar corporations. The lesson is that breakthroughs in fundamental physics, both theoretical and experimental, have always led to profound technological wealth-creating industries and will continue to do so. There is now a new revolution brewing in quantum mechanics that can be divided into three periods. The first quantum revolution was from 1900 to about 1975. The second quantum information/computer revolution was from about 1975 to 2015. (The early part of this story is told by Kaiser in his book, How the Hippies Saved Physics, how a small group of Berkeley/San Francisco physicists triggered that second revolution.) The third quantum revolution is how an extension of quantum mechanics may lead to the understanding of consciousness as a natural physical phenomenon that can emerge in many material substrates, not only in our carbon-based biochemistry. In particular, this new post-quantum mechanics may lead to naturally conscious artificial intelligence in nano-electronic machines, as well as perhaps extending human life spans to hundreds of years and more.
Two-body quantum mechanical problem on spheres
2005-01-01
The quantum mechanical two-body problem with a central interaction on the sphere ${\\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.
Quantum chemical investigation of mechanisms of silane oxidation
DEFF Research Database (Denmark)
Mader, Mary M.; Norrby, Per-Ola
2001-01-01
Several mechanisms for the peroxide oxidation of organosilanes to alcohols are compared by quantum chemical calculations, including solvation with the PCM method. Without doubt, the reaction proceeds via anionic, pentacoordinate silicate species, but a profound difference is found between in vacuo...
Quantum-chemical calculations of dye-sensitized semiconductor nanocrystals
Persson, P.; Lundqvist, M. J.; Nilsing, M.; van Duin, A. C. T.; Goddard, W. A., III
2006-08-01
Quantum chemical calculations providing detailed information of dye-sensitized semiconductor nanocrystals are presented. The calculations are used to elucidate both structural and electronic properties of photoelectrochemical devices, such as environmentally friendly Dye-Sensitized Solar Cells (DSSCs), at the molecular level. Quantum chemical calculations have recently been performed on both organic and organometallic dye molecules attached to titanium dioxide (TiO II) nanocrystals via different anchor and spacer groups. Strategies to make accurate quantum chemical calculations, e.g. at the DFT level of theory, on increasingly realistic models of such dye-sensitized semiconductor interfaces are presented. The ability of different anchor and spacer groups to act as mediators of ultrafast photo-induced electron injection from the dye molecules into the semiconductor nanocrystals is, in particular, discussed in terms of calculated electronic coupling strengths, and direct comparisons with experimental information are made whenever possible. Progress in the development of multi-scale simulation techniques using so called reactive force fields is illustrated for dye-sensitized solar cell systems.
Quantum mechanics: Thought experiments made real
Martín, Fernando
2015-02-01
Elegant experiments performed with X-rays and a double slit formed from molecular oxygen have finally made it possible to realize and test a long-standing and famous gedanken experiment in quantum mechanics.
Supersymmetric q-deformed quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
2012-06-27
A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.
Beyond Quantum Mechanics and General Relativity
Gregori, Andrea
2010-01-01
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
Four formulations of noncommutative quantum mechanics
Gouba, Laure
2016-01-01
Four formulations of noncommutative quantum mechanics are reviewed. These are the canonical, path-integral, Weyl-Wigner and systematic formulations. The four formulations are charaterized by a deformed Heisenberg algebra but differ in mathematical and conceptual overview.
Advanced quantum mechanics materials and photons
Dick, Rainer
2016-01-01
In this updated and expanded second edition of a well-received and invaluable textbook, Prof. Dick emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. Advanced Quantum Mechanics, Materials and Photons can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. This second edition includes an additional 62 new problems as well as expanded sections on relativistic quantum fields and applications of�...
Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation.
Polyak, Iakov; Benighaus, Tobias; Boulanger, Eliot; Thiel, Walter
2013-08-14
The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.
On the geometrization of quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Tavernelli, Ivano, E-mail: ita@zurich.ibm.com
2016-08-15
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.
Macroscopic quantum mechanics in a classical spacetime.
Yang, Huan; Miao, Haixing; Lee, Da-Shin; Helou, Bassam; Chen, Yanbei
2013-04-26
We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.
Uncertainty in quantum mechanics: faith or fantasy?
Penrose, Roger
2011-12-13
The word 'uncertainty', in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very 'truth' into question. This article addresses the issue of quantum 'uncertainty' from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications.
Computational approach for calculating bound states in quantum field theory
Lv, Q. Z.; Norris, S.; Brennan, R.; Stefanovich, E.; Su, Q.; Grobe, R.
2016-09-01
We propose a nonperturbative approach to calculate bound-state energies and wave functions for quantum field theoretical models. It is based on the direct diagonalization of the corresponding quantum field theoretical Hamiltonian in an effectively discretized and truncated Hilbert space. We illustrate this approach for a Yukawa-like interaction between fermions and bosons in one spatial dimension and show where it agrees with the traditional method based on the potential picture and where it deviates due to recoil and radiative corrections. This method permits us also to obtain some insight into the spatial characteristics of the distribution of the fermions in the ground state, such as the bremsstrahlung-induced widening.
Experimental status of quaternionic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Brumby, S.P.; Joshi, G.C.
1995-10-01
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. The only direct search for quaternionic quantum mechanics yet carried out is reviewed and is proposed to look for quaternionic effects in correlated multi-particle systems. It is also discussed how such experiments might distinguish between the several quaternionic models proposed in the literature. 21 refs.
Implications of conformal symmetry in quantum mechanics
Okazaki, Tadashi
2017-09-01
In conformal quantum mechanics with the vacuum of a real scaling dimension and with a complete orthonormal set of energy eigenstates, which is preferable under the unitary evolution, the dilatation expectation value between energy eigenstates monotonically decreases along the flow from the UV to the IR. In such conformal quantum mechanics, there exist bounds on scaling dimensions of the physical states and the gauge operators.
Some Mutant Forms of Quantum Mechanics
Takeuchi, Tatsu; Lewis, Zachary; Minic, Djordje
2013-01-01
We construct a `mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative `mutation' is also suggested.
Antonio Gramsci's Reflection on Quantum Mechanics
Tassani, Isabella
2006-06-01
As the first step of a wider historical reconstruction of the reception of quantum mechanics in the nineteenth-century philosophy, we are going to consider Antonio Gramsci's philosophy. He asks himself about the nature of quantum objects, if their existence depends on the act of measuring by the experimenter and if this kind of relationship can be interpreted as an argument in favour of an immaterialistic philosophy. We will remark how an idealistic interpretation of quantum mechanics found a fertile field in the Italian culture, characterized by an antiscientific attitude and at the same time needing to find in science a term of comparison.
Horizon quantum mechanics of rotating black holes
Energy Technology Data Exchange (ETDEWEB)
Casadio, Roberto [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Giugno, Andrea [Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Giusti, Andrea [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Micu, Octavian [Institute of Space Science, Bucharest, P.O. Box MG-23, Bucharest-Magurele (Romania)
2017-05-15
The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general space-times with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries. (orig.)
Quantum mechanics of charged particle beam optics
Khan, Sameen Ahmed
2018-01-01
Theory of charged particle beam optics is basic to the design and working of charged particle beam devices from electron microscopes to accelerator machines. Traditionally, the optical elements of the devices are designed and operated based on classical mechanics and classical electromagnetism, and only certain specific quantum mechanical aspects are dealt with separately using quantum theory. This book provides a systematic approach to quantum theory of charged particle beam optics, particularly in the high energy cases such as accelerators or high energy electron microscopy.
Book Review Bohmian Mechanics and Quantum Theory
Jäger, G
1999-01-01
A review of "Bohmian Mechanics and Quantum Theory: An Appraisal" (James Cushing, Arthur Fine and Sheldon Goldstein, Eds.), an extensive collection of articles on Bohmian mechanics. In addition to broad, critical overviews of Bohmian mechanics, the reviewed collection contains extensions and hybrid versions of the theory, as are several detailed applications to practical situtations.
Infinite variance in fermion quantum Monte Carlo calculations.
Shi, Hao; Zhang, Shiwei
2016-03-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.
Infinite variance in fermion quantum Monte Carlo calculations
Shi, Hao; Zhang, Shiwei
2016-03-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.
Lecture Notes in Quantum Mechanics
Cohen, D
2006-01-01
These lecture notes cover undergraduate textbook topics (e.g. as in Sakurai), and also additional advanced topics at the same level of presentation. In particular: EPR and Bell; Basic postulates; The probability matrix; Measurement theory; Entanglement; Quantum computation; Wigner-Weyl formalism; The adiabatic picture; Berry phase; Linear response theory; Kubo formula; Modern approach to scattering theory with mesoscopic orientation; Theory of the resolvent and the Green function; Gauge and Galilei Symmetries; Motion in magnetic field; Quantum Hall effect; Quantization of the electromagnetic field; Fock space formalism.
A new interpretation of quantum mechanics
Golovko, V A
2016-01-01
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields, interaction with a measuring apparatus inclusive, in a deterministic manner without any jumps. Quantum mechanics is an approximate theory because its equations follow from the above equations upon neglecting the self-field of the electron itself. Just this leads to paradoxes, seeming contradictions and jumps in quantum mechanics. The quantum mechanical wavefunction has a dual interpretation. In some problems the square of its modulus represents a real distribution of the electronic density while in others the same square determines the probability distribution of coordinates. It is shown why, given the different interpretations of the wavefunction, it satisfies one and the same Dirac or Schr\\"odinger equation. Description of many-electron systems is also considered in the star...
Jensen, L; Swart, M; van Duijnen, PT
2005-01-01
A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to mac
Quantum Monte Carlo calculations with chiral effective field theory interactions.
Gezerlis, A; Tews, I; Epelbaum, E; Gandolfi, S; Hebeler, K; Nogga, A; Schwenk, A
2013-07-19
We present the first quantum Monte Carlo (QMC) calculations with chiral effective field theory (EFT) interactions. To achieve this, we remove all sources of nonlocality, which hamper the inclusion in QMC calculations, in nuclear forces to next-to-next-to-leading order. We perform auxiliary-field diffusion Monte Carlo (AFDMC) calculations for the neutron matter energy up to saturation density based on local leading-order, next-to-leading order, and next-to-next-to-leading order nucleon-nucleon interactions. Our results exhibit a systematic order-by-order convergence in chiral EFT and provide nonperturbative benchmarks with theoretical uncertainties. For the softer interactions, perturbative calculations are in excellent agreement with the AFDMC results. This work paves the way for QMC calculations with systematic chiral EFT interactions for nuclei and nuclear matter, for testing the perturbativeness of different orders, and allows for matching to lattice QCD results by varying the pion mass.
Oss, Stefano; Rosi, Tommaso
2015-01-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many…
How to teach quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Passon, Oliver [Fachbereich Physik, University of Wuppertal, Postfach 100127, 42097 Wuppertal (Germany)
2004-11-01
In the spirit and style of John S Bell's well-known paper on How to teach special relativity it is argued that a 'Bohmian pedagogy' provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter.
Oss, Stefano; Rosi, Tommaso
2015-01-01
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many…
Energy Technology Data Exchange (ETDEWEB)
Tucker, Jon R.; Magyar, Rudolph J.
2012-02-01
High explosives are an important class of energetic materials used in many weapons applications. Even with modern computers, the simulation of the dynamic chemical reactions and energy release is exceedingly challenging. While the scale of the detonation process may be macroscopic, the dynamic bond breaking responsible for the explosive release of energy is fundamentally quantum mechanical. Thus, any method that does not adequately describe bonding is destined to lack predictive capability on some level. Performing quantum mechanics calculations on systems with more than dozens of atoms is a gargantuan task, and severe approximation schemes must be employed in practical calculations. We have developed and tested a divide and conquer (DnC) scheme to obtain total energies, forces, and harmonic frequencies within semi-empirical quantum mechanics. The method is intended as an approximate but faster solution to the full problem and is possible due to the sparsity of the density matrix in many applications. The resulting total energy calculation scales linearly as the number of subsystems, and the method provides a path-forward to quantum mechanical simulations of millions of atoms.
Calculating Casimir Energies in Renormalizable Quantum Field Theory
Milton, K A
2003-01-01
Quantum vacuum energy has been known to have observable consequences since 1948 when Casimir calculated the force of attraction between parallel uncharged plates, a phenomenon confirmed experimentally with ever increasing precision. Casimir himself suggested that a similar attractive self-stress existed for a conducting spherical shell, but Boyer obtained a repulsive stress. Other geometries and higher dimensions have been considered over the years. Local effects, and divergences associated with surfaces and edges have been considered by several authors. Quite recently, Graham et al. have re-examined such calculations, using conventional techniques of perturbative quantum field theory to remove divergences, and have suggested that previous self-stress results may be suspect. Here we show that the examples considered in their work are misleading; in particular, it is well-known that in two dimensions a circular boundary has a divergence in the Casimir energy for massless fields, while for general dimension $D$...
Tensor RG calculations and quantum simulations near criticality
Meurice, Y; Tsai, Shan-Wen; Unmuth-Yockey, J; Yang, Li-Ping; Zhang, Jin
2016-01-01
We discuss the reformulation of the O(2) model with a chemical potential and the Abelian Higgs model on a 1+1 dimensional space-time lattice using the Tensor Renormalization Group (TRG) method. The TRG allows exact blocking and connects smoothly the classical Lagrangian approach to the quantum Hamiltonian approach. We calculate the entanglement entropy in the superfluid phase of the O(2) model and show that it approximately obeys the logarithmic Calabrese-Cardy scaling obtained from Conformal Field Theory (CFT). We calculate the Polyakov loop in the Abelian Higgs model and discuss the possibility of a deconfinement transition at finite volume. We propose Bose-Hubbard Hamiltonians implementable on optical lattices as quantum simulators for CFT models.
Quantum approach to classical statistical mechanics.
Somma, R D; Batista, C D; Ortiz, G
2007-07-20
We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.
Nonrelativistic Quantum Mechanics with Fundamental Environment
Gevorkyan, Ashot S.
2011-03-01
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ R { ξ}, where R 3 and R { ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.
Quantum Mechanical Nature in Liquid NMR Quantum Computing
Institute of Scientific and Technical Information of China (English)
LONGGui－Lu; YANHai－Yang; 等
2002-01-01
The quantum nature of bulk ensemble NMR quantum computing-the center of recent heated debate,is addressed.Concepts of the mixed state and entanglement are examined,and the data in a two-qubit liquid NMR quantum computation are analyzed.the main points in this paper are;i) Density matrix describes the "state" of an average particle in an ensemble.It does not describe the state of an individual particle in an ensemble;ii) Entanglement is a property of the wave function of a microscopic particle(such as a molecule in a liquid NMR sample),and separability of the density matrix canot be used to measure the entanglement of mixed ensemble;iii) The state evolution in bulkensemble NMR quantum computation is quantum-mechanical;iv) The coefficient before the effective pure state density matrix,ε,is a measure of the simultaneity of the molecules in an ensemble,It reflets the intensity of the NMR signal and has no significance in quantifying the entanglement in the bulk ensemble NMR system.The decomposition of the density matrix into product states is only an indication that the ensemble can be prepared by an ensemble with the particles unentangeld.We conclude that effective-pure-state NMR quantum computation is genuine,not just classical simulations.
Applications of computational quantum mechanics
Temel, Burcin
This original research dissertation is composed of a new numerical technique based on Chebyshev polynomials that is applied on scattering problems, a phenomenological kinetics study for CO oxidation on RuO2 surface, and an experimental study on methanol coupling with doped metal oxide catalysts. Minimum Error Method (MEM), a least-squares minimization method, provides an efficient and accurate alternative to solve systems of ordinary differential equations. Existing methods usually utilize matrix methods which are computationally costful. MEM, which is based on the Chebyshev polynomials as a basis set, uses the recursion relationships and fast Chebyshev transforms which scale as O(N). For large basis set calculations this provides an enormous computational efficiency in the calculations. Chebyshev polynomials are also able to represent non-periodic problems very accurately. We applied MEM on elastic and inelastic scattering problems: it is more efficient and accurate than traditionally used Kohn variational principle, and it also provides the wave function in the interaction region. Phenomenological kinetics (PK) is widely used in industry to predict the optimum conditions for a chemical reaction. PK neglects the fluctuations, assumes no lateral interactions, and considers an ideal mix of reactants. The rate equations are tested by fitting the rate constants to the results of the experiments. Unfortunately, there are numerous examples where a fitted mechanism was later shown to be erroneous. We have undertaken a thorough comparison between the phenomenological equations and the results of kinetic Monte Carlo (KMC) simulations performed on the same system. The PK equations are qualitatively consistent with the KMC results but are quantitatively erroneous as a result of interplays between the adsorption and desorption events. The experimental study on methanol coupling with doped metal oxide catalysts demonstrates the doped metal oxides as a new class of catalysts
Measurements and mathematical formalism of quantum mechanics
Slavnov, D. A.
2007-03-01
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.
Nilpotent Quantum Mechanics: Analogs and Applications
Directory of Open Access Journals (Sweden)
Peter Marcer
2017-07-01
Full Text Available The most significant characteristic of nilpotent quantum mechanics is that the quantum system (fermion state and its environment (vacuum are, in mathematical terms, mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has applications well beyond quantum physics. The nilpotent structure has also been identified as being constructed from two commutative vector spaces. This zero square-root construction has a number of identifiable characteristics which we can expect to find in systems where self-organization is dominant, and a case presented after the publication of a paper by us on “The ‘Logic’ of Self-Organizing Systems” [1], in the organization of the neurons in the visual cortex. We expect to find many more complex systems where our general principles, based, by analogy, on nilpotent quantum mechanics, will apply.
On Time. 6b: Quantum Mechanical Time
Raju, C K
2008-01-01
The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure of time. This corresponds to a change of logic at the microphysical level. We show that the resulting logic is a quantum logic. This provides a natural and rigorous explanation of quantum interference. This structured-time interpretation of quantum mechanics is briefly compared with various other interpretations of q.m.
The canonical connection in quantum mechanics
Lévai, Peter; Tsutsui, I; Levay, Peter; McMullan, David; Tsutsui, Izumi
1995-01-01
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry's phase, can also be found in systems which have slow variables taking values in such a coset space.
The canonical connection in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Levay, P. [Budapesti Mueszaki Egyetem, Budapest (Hungary); Mcmullan, D.; Tsutsui, Izumi
1995-04-01
In this paper we investigate the form of induced gauge fields that arises in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G-invariance is central to the emergence of the H-connection as induced gauge fields in the different quantum sectors. We then demonstrate why the same connection, now giving rise to the non-abelian generalization of Berry`s phase, can also be found in systems which have slow variables taking values in such a coset space. (author).
Why Quantum Mechanics is Hard to Understand
Bilodeau, D
1998-01-01
To understand the foundations of quantum mechanics, we have to think carefully about how theoretical concepts are rooted in -- and limited by -- the nature of experience, as Bohr attempted to show. Geometrical pictures of physical phenomena are favored because of their clarity. Quantum phenomena, however, do not permit them. Instead, the historical and dynamical aspects of description diverge and must be expressed in different but complementary languages. Objective historical facts are recorded in terms of objects, which necessarily have an imprecise, empirical quality. Dynamics is based on quantitative abstraction from recurring patterns. The "quantum of action" is the discontinuity between these two ways of looking at the physical world.
Emergent quantum mechanics of finances
Nastasiuk, Vadim A.
2014-06-01
This paper is an attempt at understanding the quantum-like dynamics of financial markets in terms of non-differentiable price-time continuum having fractal properties. The main steps of this development are the statistical scaling, the non-differentiability hypothesis, and the equations of motion entailed by this hypothesis. From perspective of the proposed theory the dynamics of S&P500 index are analyzed.
Fourier's Law in Quantum Mechanics
Seligman, Thomas H
2010-01-01
We derive Fourier's law for a completely coherent quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the length of the system.
Semenov, Alexander; Babikov, Dmitri
2014-01-16
For computational treatment of rotationally inelastic scattering of molecules, we propose to use the mixed quantum/classical theory, MQCT. The old idea of treating translational motion classically, while quantum mechanics is used for rotational degrees of freedom, is developed to the new level and is applied to Na + N2 collisions in a broad range of energies. Comparison with full-quantum calculations shows that MQCT accurately reproduces all, even minor, features of energy dependence of cross sections, except scattering resonances at very low energies. The remarkable success of MQCT opens up wide opportunities for computational predictions of inelastic scattering cross sections at higher temperatures and/or for polyatomic molecules and heavier quenchers, which is computationally close to impossible within the full-quantum framework.
Advanced quantum mechanics materials and photons
Dick, Rainer
2012-01-01
Advanced Quantum Mechanics: Materials and Photons is a textbook which emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. The textbook can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible, Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquir...
On quantum statistical mechanics; A study guide
Majewski, W. A.
2016-01-01
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical mechanics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in the analysis of large quantum systems, and their consequences. These include the emergence of algebraic approach and the necessity of employment of infinite dimensional structures. As an illustration, a quantization of stochastic processes, new formalism...
Quantum mechanics: why complex Hilbert space?
Cassinelli, G; Lahti, P
2017-11-13
We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).
The conceptual foundations of quantum mechanics
Eisenbud, Leonard
2007-01-01
This book provides a clear and logical path to understanding what quantum mechanics is about. It will be accessible to undergraduates with minimal mathematical preparation: all that is required is an open mind, a little algebra, and a first course in undergraduate physics. Quantum mechanics is arguably the most successful physical theory. It makes predictions of incredible accuracy. It provides the structure underlying all of our electronic technology, and much of our mastery over materials. But compared with Newtonian mechanics, or even relativity, its teachings seem obscure-they have no coun
Observations of the Ramsauer-Townsend effect in quaternionic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Sobhani, Hadi [Damghan Branch, Islamic Azad University, Young Researchers and Elite Club, Damghan (Iran, Islamic Republic of); Hassanabadi, Hassan [Shahrood University of Technology, Physics Department (Iran, Islamic Republic of); Chung, Won Sang [Gyeongsang National University, Department of Physics and Research Institute of Natural Science, College of Natural Science, Jinju (Korea, Republic of)
2017-06-15
In this article, one of the well-known effects in quantum mechanics is addressed and also the extended form of quantum mechanics which is based on quaternions is presented. In the presence of this version of quantum mechanics the Ramsauer-Townsend effect has been investigated and the existence of this phenomenon is studied according to quaternionic calculations; results are presented by graphs. (orig.)
The mathematical basis for deterministic quantum mechanics
Hooft, G. 't
2006-01-01
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint
The mathematical basis for deterministic quantum mechanics
Hooft, G. 't
2007-01-01
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is
Intrinsic resonance representation of quantum mechanics
DEFF Research Database (Denmark)
Carioli, M.; Heller, E.J.; Møller, Klaus Braagaard
1997-01-01
an optimal representation, based purely on classical mechanics. ''Hidden'' constants of the motion and good actions already known to the classical mechanics are thus incorporated into the basis, leaving the quantum effects to be isolated and included by small matrix diagonalizations. This simplifies...
Presenting Nonreflexive Quantum Mechanics: Formalism and Metaphysics
Krause, Decio
2015-01-01
Nonreflexive quantum mechanics is a formulation of quantum theory based on a non-classical logic termed \\ita{nonreflexive logic} (a.k.a. `non-reflexive'). In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are \\ita{non-individuals} in some sense, and also to take into account the fact that they may be absolutely indistinguishable (or indiscernible). The nonreflexive formulation of quantum theory assumes these features of the objects already at the level of the underlying logic, so that no use is required of symmetrization postulates or other mathematical devices that serve to pretend that the objects are indiscernible (when they are not: all objects that obey classical logic are \\ita{individuals} in a sense). Here, we present the ideas of the development of nonreflexive quantum mechanics an...
Calculations in fundamental physics mechanics and heat
Heddle, T
2013-01-01
Calculations in Fundamental Physics, Volume I: Mechanics and Heat focuses on the mechanisms of heat. The manuscript first discusses motion, including parabolic, angular, and rectilinear motions, relative velocity, acceleration of gravity, and non-uniform acceleration. The book then discusses combinations of forces, such as polygons and resolution, friction, center of gravity, shearing force, and bending moment. The text looks at force and acceleration, energy and power, and machines. Considerations include momentum, horizontal or vertical motion, work and energy, pulley systems, gears and chai
Logic and probability in quantum mechanics
1976-01-01
During the academic years 1972-1973 and 1973-1974, an intensive sem inar on the foundations of quantum mechanics met at Stanford on a regular basis. The extensive exploration of ideas in the seminar led to the org~ization of a double issue of Synthese concerned with the foundations of quantum mechanics, especially with the role of logic and probability in quantum meChanics. About half of the articles in the volume grew out of this seminar. The remaining articles have been so licited explicitly from individuals who are actively working in the foun dations of quantum mechanics. Seventeen of the twenty-one articles appeared in Volume 29 of Syn these. Four additional articles and a bibliography on -the history and philosophy of quantum mechanics have been added to the present volume. In particular, the articles by Bub, Demopoulos, and Lande, as well as the second article by Zanotti and myself, appear for the first time in the present volume. In preparing the articles for publication I am much indebted to ...
Quantum mechanics and quantum information a guide through the quantum world
Fayngold, Moses
2013-01-01
Alongside a thorough definition of the basic concepts and their interrelations, backed by numerous examples, this textbook features a rare discussion of the quantum information theory. It also deals with other important topics hardly found in the literature, including the Robertson-Schrodinger-relation, angle and angular momentum uncertainties, interaction-free measurements, and the limitations of the no-cloning theorem With its interpretations of quantum mechanics and its discussions of quantum computing, this book is poised to become the standard textbook for advanced undergraduate and beginning graduate quantum mechanics courses and as an essential reference for physics students and physics professionals.
Quantum mechanics in an evolving Hilbert space
Artacho, Emilio; O'Regan, David D.
2017-03-01
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives in the context of differential geometry, thereby obtaining a more transparent formalization, and a geometrical perspective for better understanding the resulting equations. The effect of the evolution of the basis set within the spanned Hilbert space separates explicitly from the effect of the turning of the space itself when moving in parameter space, as the tangent space turns when moving in a curved space. New insights are obtained using familiar concepts in that context such as the Riemann curvature. The differential geometry is not strictly that for curved spaces as in general relativity, a more adequate mathematical framework being provided by fiber bundles. The language used here, however, will be restricted to tensors and basic quantum mechanics. The local gauge implied by a smoothly varying basis set readily connects with Berry's formalism for geometric phases. Generalized expressions for the Berry connection and curvature are obtained for a parameter-dependent occupied Hilbert space spanned by nonorthogonal Wannier functions. The formalism is applicable to basis sets made of atomic-like orbitals and also more adaptative moving basis functions (such as in methods using Wannier functions as intermediate or support bases), but should also apply to other situations in which nonorthogonal functions or related projectors should arise. The formalism is applied to the time-dependent quantum evolution of electrons for moving atoms. The geometric insights provided here allow us to propose new finite-difference time integrators, and also better understand those already proposed.
Quantum Mechanics as Quantum Information (and only a little more)
Fuchs, C
2002-01-01
In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears better calibrated for a direct assault than quantum information theory. Far from a strained application of the latest fad to a time-honored problem, this method holds promise precisely because a large part--but not all--of the structure of quantum theory has always concerned information. It is just that the physics community needs reminding. This paper, though taking quant-ph/0106166 as its core, corrects one mistake and offers several observations beyond the previous version. In particular, I identify one element of quantum mechanics that I would not label a subjective term in the theory--it is the in...
Relating the quantum mechanics of discrete systems to standard canonical quantum mechanics
Hooft, Gerard t
2012-01-01
Discrete quantum mechanics is here defined to be a quantum theory of wave functions defined on integers P_i and Q_i, while canonical quantum mechanics is assumed to be based on wave functions on the real numbers, R^n. We study reversible mappings from the position operators q_i and their quantum canonical operators p_i of a canonical theory, onto the discrete, commuting operators Q_i and P_i. In this paper we are particularly interested in harmonic oscillators. In the discrete system, these t...
Institute of Scientific and Technical Information of China (English)
Liu Yu-Min; Yu Zhong-Yuan
2009-01-01
Calculations of electronic structures about the semiconductor quantum dot and the semiconductor quantum ring are presented in this paper. To reduce the calculation costs, for the quantum dot and the quantum ring, their simplified axially symmetric shapes are utilized in our analysis. The energy dependent effective mass is taken into account in solving the Schrodinger equations in the single band effective mass approximation. The calculated results show that the energy dependent effective mass should be considered only for relatively small volume quantum dots or small quantum rings. For large size quantum materials, both the energy dependent effective mass and the parabolic effective mass can give the same results. The energy states and the effective masses of the quantum dot and the quantum ring as a function of geometric parameters are also discussed in detail.
The cellular automaton interpretation of quantum mechanics
't Hooft, Gerard
2016-01-01
This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The book presents examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of...
Multichannel framework for singular quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Camblong, Horacio E., E-mail: camblong@usfca.edu [Department of Physics and Astronomy, University of San Francisco, San Francisco, CA 94117-1080 (United States); Epele, Luis N., E-mail: epele@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Fanchiotti, Huner, E-mail: huner@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); García Canal, Carlos A., E-mail: garcia@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Ordóñez, Carlos R., E-mail: ordonez@uh.edu [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States)
2014-01-15
A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.
Non-locality beyond quantum mechanics
Popescu, Sandu
2010-01-01
Quantum mechanics is, without any doubt, a tremendously successful theory: it started by explaining black-body radiation and the photoelectric effect, it explained the spectra of atoms, and then went on to explain chemical bonds, the structure of atoms and of the atomic nucleus, the properties of crystals and the elementary particles, and a myriad of other phenomena. Yet it is safe to say that we still lack a deep understanding of quantum mechanics – surprising and even puzzling new effects continue to be discovered with regularity. That we are surprised and puzzled is the best sign that we still don't understand; however, the veil over the mysteries of quantum mechanics is starting to lift a little.
Holism, Physical Theories and Quantum Mechanics
Seevinck, M P
2004-01-01
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. I propose an operational criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if some determination (measurement) of the global properties in the theory which can be determined by global measurements, can not be implemented by local operations and classical communication. This approach is contrasted with the well known approaches to holism in terms of supervenience. I will argue that the latter have a limited scope and need to be extended using the criterion for holism proposed here in order to satisfactory address the issue for physical theories. I formalize this criterion for classical particle physics and Bohmian mechanics as represented on a Cartesian phase and configuration space, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum ope...
Introductory quantum mechanics for applied nanotechnology
Kim, Dae Mann
2015-01-01
This introductory textbook covers fundamental quantum mechanics from an application perspective, considering optoelectronic devices, biological sensors and molecular imagers as well as solar cells and field effect transistors. The book provides a brief review of classical and statistical mechanics and electromagnetism, and then turns to the quantum treatment of atoms, molecules, and chemical bonds. Aiming at senior undergraduate and graduate students in nanotechnology related areas like physics, materials science, and engineering, the book could be used at schools that offer interdisciplinary but focused training for future workers in the semiconductor industry and for the increasing number of related nanotechnology firms, and even practicing people could use it when they need to learn related concepts. The author is Professor Dae Mann Kim from the Korea Institute for Advanced Study who has been teaching Quantum Mechanics to engineering, material science and physics students for over 25 years in USA and Asia.
Precision decay rate calculations in quantum field theory
Andreassen, Anders; Frost, William; Schwartz, Matthew D
2016-01-01
Tunneling in quantum field theory is worth understanding properly, not least because it controls the long term fate of our universe. There are however, a number of features of tunneling rate calculations which lack a desirable transparency, such as the necessity of analytic continuation, the appropriateness of using an effective instead of classical potential, and the sensitivity to short-distance physics. This paper attempts to review in pedagogical detail the physical origin of tunneling and its connection to the path integral. Both the traditional potential-deformation method and a recent more direct propagator-based method are discussed. Some new insights from using approximate semi-classical solutions are presented. In addition, we explore the sensitivity of the lifetime of our universe to short distance physics, such as quantum gravity, emphasizing a number of important subtleties.
Calculation of hyperfine interaction in spherical quantum dot
Yakar, Yusuf; Çakır, Bekir; Özmen, Ayhan
2015-10-01
In this study, we have calculated the unperturbed wavefunctions and energy eigenvalues of the ground and excited states of a spherical quantum dot, GaAs/AlxGa1-xAs, by using quantum genetic algorithm and Hartree-Fock Roothaan method. Hyperfine coupling constant and hyperfine energy of 1s, 2p, 3d and 4f levels are carried out as a function of dot radius. The results show that the hyperfine constant and hyperfine energy varies rapidly in the strong and medium confining regions as dot radius decreases. It is worth pointing out that dot radius, impurity charge and angular momentum have a strong influence on the hyperfine energy. It is also found that hyperfine energy and hyperfine splitting vary with aluminium concentration ratio x.
Delay time calculation for dual-wavelength quantum cascade lasers
Energy Technology Data Exchange (ETDEWEB)
Hamadou, A., E-mail: abd-hamado@yahoo.fr [Département des Sciences et Techniques, Faculté des Sciences et de la Technologie, Université de Bordj Bou Arreridj 34000 (Algeria); Laboratoire d’étude des surfaces et interfaces des matériaux solides (LESIMS), Sétif 19000 (Algeria); Lamari, S. [Laboratoire d’étude des surfaces et interfaces des matériaux solides (LESIMS), Sétif 19000 (Algeria); Département de Physique, Faculté des Sciences, Université Sétif 1, 19000 (Algeria); Thobel, J.-L. [Institut d' Electronique, de Microélectronique et de Nanotechnologie (IEMN), UMR 8520, Université Lille1, Avenue Poincaré, BP 60069, 59652 Villeneuve d' Ascq Cédex (France)
2013-11-28
In this paper, we calculate the turn-on delay (t{sub th}) and buildup (Δt) times of a midinfrared quantum cascade laser operating simultaneously on two laser lines having a common upper level. The approach is based on the four-level rate equations model describing the variation of the electron number in the states and the photon number present within the cavity. We obtain simple analytical formulae for the turn-on delay and buildup times that determine the delay times and numerically apply our results to both the single and bimode states of a quantum cascade laser, in addition the effects of current injection on t{sub th} and Δt are explored.
Calculation and Improvement on External Quantum Efficiency of OLEDs
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The calculation of the external quantum efficiency(ηext) of organic light-emitting devices(OLEDs) is presented theoretically. The basic idea is to obtain ηext by calculating the fraction of the generated light that can escape through the top surface and the average transmittance over the escape cone. During the calculation, the effects of the interference, absorption and multiple reflections are neglected. Then a result of a typical 8-tris-hydroxyquinoline aluminum(Alq3)-based OLEDs on a planar glass substrate is obtained. And a twice increase in ηext can be achieved by using a high-index-glass substrate with an antireflection coating(SiO2) on substrate surface.
Spectroscopic and quantum chemical calculation study on 2-ethoxythiazole molecule
Avcı, Davut; Dede, Bülent; Bahçeli, Semiha; Varkal, Döndü
2017-06-01
In this study, the 2-ethoxythiazole molecule (C5H7NSO) which is a member of the five-membered heterocyles with one nitrogen atom group has been investigated by using the experimental UV-vis (in three different solvents) and FT-IR spectral results as well as some magnetic properties. Furthermore, the calculated molecular geometric parameters, vibrational wavenumbers, HOMO-LUMO energies, 1H and 13C NMR chemical shift values and natural bond orbitals (NBO) of the title molecule have been calculated at the B3LYP and HSEH1PBE levels of theory with the 6-311++G(d,p) basis set. The spectral results obtained from the quantum chemical calculations are in good agreement with the experimental results.
Gallilei covariant quantum mechanics in electromagnetic fields
Directory of Open Access Journals (Sweden)
H. E. Wilhelm
1985-01-01
Full Text Available A formulation of the quantum mechanics of charged particles in time-dependent electromagnetic fields is presented, in which both the Schroedinger equation and wave equations for the electromagnetic potentials are Galilei covariant, it is shown that the Galilean relativity principle leads to the introduction of the electromagnetic substratum in which the matter and electromagnetic waves propagate. The electromagnetic substratum effects are quantitatively significant for quantum mechanics in reference frames, in which the substratum velocity w is in magnitude comparable with the velocity of light c. The electromagnetic substratum velocity w occurs explicitly in the wave equations for the electromagnetic potentials but not in the Schroedinger equation.
An Axiomatic Basis for Quantum Mechanics
Cassinelli, Gianni; Lahti, Pekka
2016-10-01
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Solér which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of Solér's theorem to the theory of symmetry in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions.
Quantum mechanics new approaches to selected topics
Lipkin, Harry J
2007-01-01
Acclaimed as ""excellent"" (Nature) and ""very original and refreshing"" (Physics Today), this collection of self-contained studies is geared toward advanced undergraduates and graduate students. Its broad selection of topics includes the Mössbauer effect, many-body quantum mechanics, scattering theory, Feynman diagrams, and relativistic quantum mechanics.Author Harry J. Lipkin, a well-known teacher at Israel's Weizmann Institute, takes an unusual approach by introducing many interesting physical problems and mathematical techniques at a much earlier point than in conventional texts. This meth
Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
Grössing, Gerhard
2015-10-01
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...
Quantum mechanical method for estimating ionicity of spinel ferrites
Energy Technology Data Exchange (ETDEWEB)
Ji, D.H. [Hebei Advanced Thin Films Laboratory, Department of Physics, Hebei Normal University, Shijiazhuang City 050024 (China); Tang, G.D., E-mail: tanggd@mail.hebtu.edu.cn [Hebei Advanced Thin Films Laboratory, Department of Physics, Hebei Normal University, Shijiazhuang City 050024 (China); Li, Z.Z.; Hou, X.; Han, Q.J.; Qi, W.H.; Liu, S.R.; Bian, R.R. [Hebei Advanced Thin Films Laboratory, Department of Physics, Hebei Normal University, Shijiazhuang City 050024 (China)
2013-01-15
The ionicity (0.879) of cubic spinel ferrite Fe{sub 3}O{sub 4} has been determined, using both experimental magnetization and density of state calculations from the density functional theory. Furthermore, a quantum mechanical estimation method for the ionicity of spinel ferrites is proposed by comparing the results from Phillips' ionicity. On the basis of this, ionicities of the spinel ferrites MFe{sub 2}O{sub 4} (M=Mn, Fe, Co, Ni, Cu) are calculated. As an application, the ion distribution at (A) and [B] sites of (A)[B]{sub 2}O{sub 4} spinel ferrites MFe{sub 2}O{sub 4} (M=Fe, Co, Ni, Cu) are calculated using current ionicity values. - Highlights: Black-Right-Pointing-Pointer The ionicity of Fe{sub 3}O{sub 4} was determined as 0.879 by the density functional theory. Black-Right-Pointing-Pointer The ionicities of spinel ferrites were estimated by a quantum mechanical method. Black-Right-Pointing-Pointer A quantum mechanical method estimating ionicity is suitable for II-VI compounds. Black-Right-Pointing-Pointer The ion distributions of MFe{sub 2}O{sub 4} are calculated by current ionicities values.
Student Ability to Distinguish between Superposition States and Mixed States in Quantum Mechanics
Passante, Gina; Emigh, Paul J.; Shaffer, Peter S.
2015-01-01
Superposition gives rise to the probabilistic nature of quantum mechanics and is therefore one of the concepts at the heart of quantum mechanics. Although we have found that many students can successfully use the idea of superposition to calculate the probabilities of different measurement outcomes, they are often unable to identify the…
Student Ability to Distinguish between Superposition States and Mixed States in Quantum Mechanics
Passante, Gina; Emigh, Paul J.; Shaffer, Peter S.
2015-01-01
Superposition gives rise to the probabilistic nature of quantum mechanics and is therefore one of the concepts at the heart of quantum mechanics. Although we have found that many students can successfully use the idea of superposition to calculate the probabilities of different measurement outcomes, they are often unable to identify the…
A new introductory quantum mechanics curriculum
Kohnle, Antje; Bozhinova, Inna; Browne, Dan; Everitt, Mark; Fomins, Aleksejs; Kok, Pieter; Kulaitis, Gytis; Prokopas, Martynas; Raine, Derek; Swinbank, Elizabeth
2014-01-01
The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum-mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of the interpretive aspects of quantum mechanics and quantum information theory. This paper gives an overview of the resources available from the IOP website. The core text includes around 80 articles which are co-authored by leading experts, arranged in themes, and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is included in the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways, from being supplemental to existing courses to forming a complete programme.
Infinite Variance in Fermion Quantum Monte Carlo Calculations
Shi, Hao
2015-01-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, lattice QCD calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied upon to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple sub-areas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations turn out to have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calc...
Quantum Gravity and a Time Operator in Relativistic Quantum Mechanics
Bauer, M
2016-01-01
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in General Relativity (GR) are seen as mutually incompatible notions. The introduction of a dy- namical time operator in relativistic quantum mechanics (RQM), that in the Heisenberg representation is also a function of the parameter t (iden- tifed as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of the canonical quantization approach toquantum gravity is developed. 1
Quantum mechanics/molecular mechanics restrained electrostatic potential fitting.
Burger, Steven K; Schofield, Jeremy; Ayers, Paul W
2013-12-05
We present a quantum mechanics/molecular mechanics (QM/MM) method to evaluate the partial charges of amino acid residues for use in MM potentials based on their protein environment. For each residue of interest, the nearby residues are included in the QM system while the rest of the protein is treated at the MM level of theory. After a short structural optimization, the partial charges of the central residue are fit to the electrostatic potential using the restrained electrostatic potential (RESP) method. The resulting charges and electrostatic potential account for the individual environment of the residue, although they lack the transferable nature of library partial charges. To evaluate the quality of the QM/MM RESP charges, thermodynamic integration is used to measure the pKa shift of the aspartic acid residues in three different proteins, turkey egg lysozyme, beta-cryptogein, and Thioredoxin. Compared to the AMBER ff99SB library values, the QM/MM RESP charges show better agreement between the calculated and experimental pK(a) values for almost all of the residues considered.
Quantum Mechanics in the Light of Quantum Cosmology
Gell-Mann, Murray; Hartle, James B.
We sketch a quantum-mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the "quasiclassical domain" of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities (approximately obeying the rules of probability theory) can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative histories of the universe. A quasiclassical domain consists of a branching set of alternative decohering histories, described by a coarse graining that is, in an appropriate sense, maximally refined consistent with decoherence, with individual branches that exhibit a high level of classical correlation in time. We pose the problem of making these notions precise and quantitative. A quasiclassical domain is emergent in the universe as a consequence of the initial condition and the action function of the elementary particles. It is an important question whether all the quasiclassical domains are roughly equivalent or whether there are various essentially inequivalent ones. A measurement is a correlation with variables in a quasiclassical domain. An "observer" (or information gathering and utilizing system) is a complex adaptive system that has evolved to exploit the relative predictability of a quasiclassical domain, or rather a set of such domains among which it cannot discriminate because of its own very coarse graining. We suggest that resolution of many of the problems of interpretation presented by quantum mechanics is to be accomplished, not by further scrutiny of the subject as it applies to reproducible laboratory situations, but rather by an examination of alternative histories of the universe, stemming from its
An Emphasis of Electron Energy Calculation in Quantum Wells
Institute of Scientific and Technical Information of China (English)
GAOShao-Wen; CAOJun-Cheng; FENGSong-Lin
2004-01-01
We investigate various methods for the calculation of the electron energy in semiconductor quantum wells and focus on a matrix algorithm method. The results show better fitness of the factor -h2/2 э/эz 1/m*（z） э/эz than that of -h2/2 1/m*（z） э2/эz2 in the first part of the Schroedinger equation. The effect of nonparabolicity in the conduction band is also discussed.
The Emergent Copenhagen Interpretation of Quantum Mechanics
Hollowood, Timothy J
2013-01-01
We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint p...
Quantum Mechanics on discrete space and time
Lorente, M
2004-01-01
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are complex functions of discrete variable. As a concrete example we develop a discrete analog of the one-dimensional quantum harmonic oscillator, using the dependence of the Wigner functions in terms of Kravchuk polynomials. In this model the position operator has a discrete spectrum given by one index of the Wigner functions, in the same way that the energy eigenvalues are given by the other matricial index. Similar picture can be made for other models where the differential equation and their solutions correspond to the continuous limit of some difference operator and orthogonal polynomial of discrete variable.
Practical quantum mechanics modern tools and applications
Manousakis, Efstratios
2016-01-01
Quantum mechanics forms the foundation of all modern physics, including atomic, nuclear, and molecular physics, the physics of the elementary particles, condensed matter physics. Modern astrophysics also relies heavily on quantum mechanics. Quantum theory is needed to understand the basis for new materials, new devices, the nature of light coming from stars, the laws which govern the atomic nucleus, and the physics of biological systems. As a result the subject of this book is a required course for most physics graduate students. While there are many books on the subject, this book targets specifically graduate students and it is written with modern advances in various fields in mind. Many examples treated in the various chapters as well as the emphasis of the presentation in the book are designed from the perspective of such problems. For example, the book begins by putting the Schrodinger equation on a spatial discrete lattice and the continuum limit is also discussed, inspired by Hamiltonian lattice gauge ...
Using quantum mechanics to synthesize electronic devices
Schmidt, Petra; Levi, Anthony
2005-03-01
Adaptive quantum design [1] has been used to explore the possibility of creating new classes of electronic semiconductor devices. We show how non-equilibrium electron transmission through a synthesized conduction band potential profile can be used to obtain a desired current - voltage characteristic. We illustrate our methodology by designing a two-terminal linear resistive element in which current is limited by quantum mechanical transmission through a potential profile and power is dissipated non-locally in the electrodes. As electronic devices scale to dimensions in which the physics of operation is dominated by quantum mechanical effects, classical designs fail to deliver the desired functionality. Our device synthesis approach is a way to realize device functionality that may not otherwise be achieved. [1] Y.Chen, R.Yu, W.Li, O.Nohadani, S.Haas, A.F.J. Levi, Journal of Applied Physics, Vol.94, No.9, p6065, 2003
Quantum and Semiclassical Calculations of Cold Atom Collisions in Light Fields
Suominen, K A; Tuvi, I; Burnett, K; Julienne, P S
1998-01-01
We derive and apply an optical Bloch equation (OBE) model for describing collisions of ground and excited laser cooled alkali atoms in the presence of near-resonant light. Typically these collisions lead to loss of atoms from traps. We compare the results obtained with a quantum mechanical complex potential treatment, semiclassical Landau-Zener models with decay, and a quantum time-dependent Monte-Carlo wave packet (MCWP) calculation. We formulate the OBE method in both adiabatic and diabatic representations. We calculate the laser intensity dependence of collision probabilities and find that the adiabatic OBE results agree quantitatively with those of the MCWP calculation, and qualitatively with the semiclassical Landau-Zener model with delayed decay, but that the complex potential method or the traditional Landau-Zener model fail in the saturation limit.
Liu, Jinfeng; Zhang, John Z H; He, Xiao
2016-01-21
Geometry optimization and vibrational spectra (infrared and Raman spectra) calculations of proteins are carried out by a quantum chemical approach using the EE-GMFCC (electrostatically embedded generalized molecular fractionation with conjugate caps) method (J. Phys. Chem. A, 2013, 117, 7149). The first and second derivatives of the EE-GMFCC energy are derived and employed in geometry optimization and vibrational frequency calculations for several test systems, including a polypeptide ((GLY)6), an α-helix (AKA), a β-sheet (Trpzip2) and ubiquitin (76 residues with 1231 atoms). Comparison of the present results with those obtained from full system QM (quantum mechanical) calculations shows that the EE-GMFCC approach can give accurate molecular geometries, vibrational frequencies and vibrational intensities. The EE-GMFCC method is also employed to simulate the amide I vibration of proteins, which has been widely used for the analysis of peptide and protein structures, and the results are in good agreement with the experimental observations.
Calculation of exchange interaction for modified Gaussian coupled quantum dots
Khordad, R.
2017-08-01
A system of two laterally coupled quantum dots with modified Gaussian potential has been considered. Each quantum dot has an electron under electric and magnetic field. The quantum dots have been considered as hydrogen-like atoms. The physical picture has translated into the Heisenberg spin Hamiltonian. The Schrödinger equation using finite element method has been numerically solved. The exchange energy factor has been calculated as a functions of electric field, magnetic field, and the separation distance between the centers of the dots ( d). According to the results, it is found that there is the transition from anti-ferromagnetic to ferromagnetic for constant electric field. Also, the transition occurs from ferromagnetic to anti-ferromagnetic for constant magnetic field (B>1 T). With decreasing the distance between the centers of the dots and increasing magnetic field, the transition occurs from anti-ferromagnetic to ferromagnetic. It is found that a switching of exchange energy factor is presented without canceling the interactions of the electric and magnetic fields on the system.
Quantum Mechanical Nature in Liquid NMR Quantum Computing
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu; YAN Hai-Yang; LI Yan-Song; TU Chang-Cun; ZHU Sheng-Jiang; RUAN Dong; SUN Yang; TAO Jia-Xun; CHEN Hao-Ming
2002-01-01
The quantum nature of bulk ensemble NMR quantum computing the center of recent heated debate,is addressed. Concepts of the mixed state and entanglement are examined, and the data in a two-qubit liquid NMRquantum computation are analyzed. The main points in this paper are: i) Density matrix describes the "state" of anaverage particle in an ensemble. It does not describe the state of an individual particle in an ensemble; ii) Entanglementis a property of the wave function of a microscopic particle (such as a molecule in a liquid NMR sample), and separabilityof the density matrix cannot be used to measure the entanglement of mixed ensemble; iii) The state evolution in bulk-ensemble NMRquantum computation is quantum-mechanical; iv) The coefficient before the effective pure state densitymatrix, e, is a measure of the simultaneity of the molecules in an ensemble. It reflects the intensity of the NMR signaland has no significance in quantifying the entanglement in the bulk ensemble NMR system. The decomposition of thedensity matrix into product states is only an indication that the ensemble can be prepared by an ensemble with theparticles unentangled. We conclude that effective-pure-state NMR quantum computation is genuine, not just classicalsimulations.
Emerging interpretations of quantum mechanics and recent progress in quantum measurement
Clarke, M. L.
2014-01-01
The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism).
Riemann hypothesis and quantum mechanics
Planat, Michel; Solé, Patrick; Omar, Sami
2011-04-01
In their 1995 paper, Jean-Benoît Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β), where β is an inverse temperature. We formulate Riemann hypothesis (RH) as a property of the low-temperature Kubo-Martin-Schwinger (KMS) states of this theory. More precisely, the expectation value of the BC phase operator can be written as \\phi _{\\beta }(q)=N_{q-1}^{\\beta -1} \\psi _{\\beta -1}(N_q), where Nq = ∏qk = 1pk is the primorial number of order q and ψb is a generalized Dedekind ψ function depending on one real parameter b as \\psi _b (q)=q \\prod _{p \\in {P,}p \\vert q}\\frac{1-1/p^b}{1-1/p}. Fix a large inverse temperature β > 2. The RH is then shown to be equivalent to the inequality N_q |\\phi _\\beta (N_q)|\\zeta (\\beta -1) \\gt e^\\gamma log log N_q, for q large enough. Under RH, extra formulas for high-temperature KMS states (1.5 < β < 2) are derived. 'Number theory is not pure Mathematics. It is the Physics of the world of Numbers.' Alf van der Poorten
Student ability to distinguish between superposition states and mixed states in quantum mechanics
Passante, Gina; Emigh, Paul J.; Shaffer, Peter S.
2015-12-01
Superposition gives rise to the probabilistic nature of quantum mechanics and is therefore one of the concepts at the heart of quantum mechanics. Although we have found that many students can successfully use the idea of superposition to calculate the probabilities of different measurement outcomes, they are often unable to identify the experimental implications of a superposition state. In particular, they fail to recognize how a superposition state and a mixed state (sometimes called a "lack of knowledge" state) can produce different experimental results. We present data that suggest that superposition in quantum mechanics is a difficult concept for students enrolled in sophomore-, junior-, and graduate-level quantum mechanics courses. We illustrate how an interactive lecture tutorial can improve student understanding of quantum mechanical superposition. A longitudinal study suggests that the impact persists after an additional quarter of quantum mechanics instruction that does not specifically address these ideas.
A new exact quantum mechanical propagator
Wiegel, F.W.; Andel, van P.W.
1987-01-01
The authors derive a closed-form expression for the time-dependent propagator for a quantum mechanical particle which is subject to an external force which is the sum of (i) a reflecting half-plane barrier with a straight edge, and (ii) a harmonic force pointing towards a point of the edge. This new
Quantum mechanics for two-timers
Indian Academy of Sciences (India)
P Mitra
2001-02-01
Extensions of standard quantum mechanics with joint probability distributions for position coordinates and momenta have been proposed in the literature. Time is assumed to be onedimensional in these studies. In view of recent interest in two-dimensional time, the construction is extended to this situation and found to satisfy the necessary consistency conditions.
Quantum Mechanical Effects in Gravitational Collapse
Greenwood, Eric
2010-01-01
In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schr\\"odinger formalism. The Functional Schr\\"odinger formalism allows us to investigate the time-dependent evolutions of the quantum mechanical effects, which is beyond the scope of the usual methods used to investigate the quantum mechanical corrections of gravitational collapse. Utilizing the time-dependent nature of the Functional Schr\\"odinger formalism, we study the quantization of a spherically symmetric domain wall from the view point of an asymptotic and infalling observer, in the absence of radiation. To build a more realistic picture, we then study the time-dependent nature of the induced radiation during the collapse using a semi-classical approach. Using the domain wall and the induced radiation, we then study the time-dependent evolution of the entropy of the domain wall. Finally we make some remarks about the pos...
Student Difficulties with Quantum Mechanics Formalism
Singh, Chandralekha
2016-01-01
We discuss student difficulties in distinguishing between the physical space and Hilbert space and difficulties related to the Time-independent Schroedinger equation and measurements in quantum mechanics. These difficulties were identified by administering written surveys and by conducting individual interviews with students.
Spin & Statistics in Nonrelativistic Quantum Mechanics, II
Kuckert, B; Kuckert, Bernd; Mund, Jens
2004-01-01
Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems and reformulated and further simplified in a more geometric language.
Holism, physical theories and quantum mechanics
Seevinck, M. P.
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.
Quantum mechanics in finite dimensional Hilbert space
de la Torre, A C
2002-01-01
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-06
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Accelerating atomistic calculations of quantum energy eigenstates on graphic cards
Rodrigues, Walter; Pecchia, A.; Lopez, M.; Auf der Maur, M.; Di Carlo, A.
2014-10-01
Electronic properties of nanoscale materials require the calculation of eigenvalues and eigenvectors of large matrices. This bottleneck can be overcome by parallel computing techniques or the introduction of faster algorithms. In this paper we report a custom implementation of the Lanczos algorithm with simple restart, optimized for graphical processing units (GPUs). The whole algorithm has been developed using CUDA and runs entirely on the GPU, with a specialized implementation that spares memory and reduces at most machine-to-device data transfers. Furthermore parallel distribution over several GPUs has been attained using the standard message passing interface (MPI). Benchmark calculations performed on a GaN/AlGaN wurtzite quantum dot with up to 600,000 atoms are presented. The empirical tight-binding (ETB) model with an sp3d5s∗+spin-orbit parametrization has been used to build the system Hamiltonian (H).
Quantum Monte Carlo Calculations of Nucleon-Nucleus Scattering
Wiringa, R. B.; Nollett, Kenneth M.; Pieper, Steven C.; Brida, I.
2009-10-01
We report recent quantum Monte Carlo (variational and Green's function) calculations of elastic nucleon-nucleus scattering. We are adding the cases of proton-^4He, neutron-^3H and proton-^3He scattering to a previous GFMC study of neutron-^4He scattering [1]. To do this requires generalizing our methods to include long-range Coulomb forces and to treat coupled channels. The two four-body cases can be compared to other accurate four-body calculational methods such as the AGS equations and hyperspherical harmonic expansions. We will present results for the Argonne v18 interaction alone and with Urbana and Illinois three-nucleon potentials. [4pt] [1] K.M. Nollett, S. C. Pieper, R.B. Wiringa, J. Carlson, and G.M. Hale, Phys. Rev. Lett. 99, 022502 (2007)
Automated quantum conductance calculations using maximally-localised Wannier functions
Shelley, Matthew; Mostofi, Arash A; Marzari, Nicola
2011-01-01
A robust, user-friendly, and automated method to determine quantum conductance in disordered quasi-one-dimensional systems is presented. The scheme relies upon an initial density- functional theory calculation in a specific geometry after which the ground-state eigenfunctions are transformed to a maximally-localised Wannier function (MLWF) basis. In this basis, our novel algorithms manipulate and partition the Hamiltonian for the calculation of coherent electronic transport properties within the Landauer-Buttiker formalism. Furthermore, we describe how short- ranged Hamiltonians in the MLWF basis can be combined to build model Hamiltonians of large (>10,000 atom) disordered systems without loss of accuracy. These automated algorithms have been implemented in the Wannier90 code[Mostofi et al, Comput. Phys. Commun. 178, 685 (2008)], which is interfaced to a number of electronic structure codes such as Quantum-ESPRESSO, AbInit, Wien2k, SIESTA and FLEUR. We apply our methods to an Al atomic chain with a Na defect...
Interactive Quantum Mechanics Quantum Experiments on the Computer
Brandt, S; Dahmen, H.D
2011-01-01
Extra Materials available on extras.springer.com INTERACTIVE QUANTUM MECHANICS allows students to perform their own quantum-physics experiments on their computer, in vivid 3D color graphics. Topics covered include: • harmonic waves and wave packets, • free particles as well as bound states and scattering in various potentials in one and three dimensions (both stationary and time dependent), • two-particle systems, coupled harmonic oscillators, • distinguishable and indistinguishable particles, • coherent and squeezed states in time-dependent motion, • quantized angular momentum, • spin and magnetic resonance, • hybridization. For the present edition the physics scope has been widened appreciably. Moreover, INTERQUANTA can now produce user-defined movies of quantum-mechanical situations. Movies can be viewed directly and also be saved to be shown later in any browser. Sections on spec...
On Quantum Mechanics on Noncommutative Quantum Phase Space
Institute of Scientific and Technical Information of China (English)
A.E.F. DjemaI; H. Smail
2004-01-01
In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM),characterized by a space noncommutativity matrix parameter θ =∈k ijθk and a momentum noncommutativity matrix parameter βij = ∈k ijβk, is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations, and secondly that the two parameters are equivalent but with opposite sign, up to a dimension factor depending on the physical system under study. This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS. Within our framework, we treat some physical systems on NCQPS : free particle, harmonic oscillator, system of two-charged particles, Hydrogen atom. Among the obtained results,we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β, representing the same particle in presence ofa magnetic field B = q-1 β. For the other examples, additional correction terms depending onβ appear in the expression of the energy spectrum. Finally, in the two-particle system case, we emphasize the fact that for two opposite charges noncommutativity is effectively feeled with opposite sign.
Quantum mechanical coherence, resonance, and mind
Energy Technology Data Exchange (ETDEWEB)
Stapp, H.P.
1995-03-26
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Global and Local Horizon Quantum Mechanics
Casadio, R; Giusti, A
2016-01-01
Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical "Hamiltonian" constraint that relates the gravitational radius to the ADM mass, thus giving rise to a "horizon wave-function". This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner-Sharp mass function of the quantum source, provided its energy spectrum is determine by spatially localised modes.
Quantum mechanics of 4-derivative theories
Energy Technology Data Exchange (ETDEWEB)
Salvio, Alberto [Universidad Autonoma de Madrid and Instituto de Fisica Teorica IFT-UAM/CSIC, Departamento de Fisica Teorica, Madrid (Spain); Strumia, Alessandro [Dipartimento di Fisica, Universita di Pisa (Italy); CERN, Theory Division, Geneva (Switzerland); INFN, Pisa (Italy)
2016-04-15
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm. (orig.)
Quantum mechanical coherence, resonance, and mind
Stapp, Henry P
1995-01-01
Norbert Wiener and J.B.S. Haldane suggested during the early thirties that the profound changes in our conception of matter entailed by quantum theory opens the way for our thoughts, and other experiential or mind-like qualities, to play a role in nature that is causally interactive and effective, rather than purely epiphenomenal, as required by classical mechanics. The mathematical basis of this suggestion is described here, and it is then shown how, by giving mind this efficacious role in natural process, the classical character of our perceptions of the quantum universe can be seen to be a consequence of evolutionary pressures for the survival of the species.
Global and local horizon quantum mechanics
Casadio, Roberto; Giugno, Andrea; Giusti, Andrea
2017-02-01
Horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical "Hamiltonian" constraint that relates the gravitational radius to the ADM mass, thus giving rise to a "horizon wave-function". This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner-Sharp mass function of the quantum source, provided its energy spectrum is determined by spatially localised modes.
Quantum mechanics of 4-derivative theories.
Salvio, Alberto; Strumia, Alessandro
2016-01-01
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.
Spinning Particles in Quantum Mechanics and Quantum Field Theory
Corradini, Olindo
2015-01-01
The first part of the lectures, given by O. Corradini, covers introductory material on quantum-mechanical Feynman path integrals, which are here derived and applied to several particle models. We start considering the nonrelativistic bosonic particle, for which we compute the exact path integrals for the case of the free particle and for the harmonic oscillator, and then describe perturbation theory for an arbitrary potential. We then move to relativistic particles, both bosonic and fermionic (spinning) particles. We first investigate them from the classical view-point, studying the symmetries of their actions, then consider their canonical quantization and path integrals, and underline the role these models have in the study of space-time quantum field theories (QFT), by introducing the "worldline" path integral representation of propagators and effective actions. We also describe a special class of spinning particles that constitute a first-quantized approach to higher-spin fields. Since the fifties the qua...
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Akhmedov, Evgeny Kh.; Kopp, Joachim
2010-01-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
A mathematical theory for deterministic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hooft, Gerard ' t [Institute for Theoretical Physics, Utrecht University (Netherlands); Spinoza Institute, Postbox 80.195, 3508 TD Utrecht (Netherlands)
2007-05-15
Classical, i.e. deterministic theories underlying quantum mechanics are considered, and it is shown how an apparent quantum mechanical Hamiltonian can be defined in such theories, being the operator that generates evolution in time. It includes various types of interactions. An explanation must be found for the fact that, in the real world, this Hamiltonian is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.
Bohmian mechanics and quantum theory an appraisal
Goldstein, Sheldon; Cushing, James T
1996-01-01
We are often told that quantum phenomena demand radical revisions of our scientific world view and that no physical theory describing well defined objects, such as particles described by their positions, evolving in a well defined way, let alone deterministically, can account for such phenomena. The great majority of physicists continue to subscribe to this view, despite the fact that just such a deterministic theory, accounting for all of the phe nomena of nonrelativistic quantum mechanics, was proposed by David Bohm more than four decades ago and has arguably been around almost since the inception of quantum mechanics itself. Our purpose in asking colleagues to write the essays for this volume has not been to produce a Festschrift in honor of David Bohm (worthy an undertaking as that would have been) or to gather together a collection of papers simply stating uncritically Bohm's views on quantum mechanics. The central theme around which the essays in this volume are arranged is David Bohm's vers...
A Calculation of Cosmological Scale from Quantum Coherence
Energy Technology Data Exchange (ETDEWEB)
Lindesay, J
2004-07-23
We use general arguments to examine the energy scales for which a quantum coherent description of gravitating quantum energy units is necessary. The cosmological dark energy density is expected to decouple from the Friedman-Lemaitre energy density when the Friedman-Robertson-Walker scale expansion becomes sub-luminal at R = c, at which time the usual microscopic interactions of relativistic quantum mechanics (QED, QCD, etc) open new degrees of freedom. We assume that these microscopic interactions cannot signal with superluminal exchanges, only superluminal quantum correlations. The expected gravitational vacuum energy density at that scale would be expected to freeze out due to the loss of gravitational coherence. We define the vacuum energy which generates this cosmological constant to be that of a zero temperature Bose condensate at this gravitational de-coherence scale. We presume a universality throughout the universe in the available degrees of freedom determined by fundamental constants during its evolution. Examining the reverse evolution of the universe from the present, long before reaching Planck scale dynamics one expects major modifications from the de-coherent thermal equations of state, suggesting that the pre-coherent phase has global coherence properties. Since the arguments presented involve primarily counting of degrees of freedom, we expect the statistical equilibrium states of causally disconnected regions of space to be independently identical. Thus, there is no horizon problem associated with the lack of causal influences between spatially separated regions in this approach. The scale of the amplitude of fluctuations produced during de-coherence of cosmological vacuum energy are found to evolve to values consistent with those observed in cosmic microwave background radiation and galactic clustering.
On the missing axiom of Quantum Mechanics
D'Ariano, G M
2005-01-01
Quantum Non Locality, ruling out an epistemic interpretation of quantum probabilities for an ontic one, elevates Quantum Mechanics to the level of a Theory of Knowledge. In such context the superposition principle becomes an unacceptable extrinsic axiom of non "gnoseological" nature. We are thus lead to seek a purely operational axiomatization that supersedes the current mathematical one based on Hilbert spaces, with the purpose of deriving the latter from the former. In the present work I present a set of axioms for a general operational approach, based on a general definition of "experiment". As we will see, this starting point logically entails a sequel of notions [state, conditional state, local state, pure state, faithful state, instrument, propensity (i.e. "effect"), dynamical and informational equivalence, dynamical and informational compatibility, predictability, discriminability, programmability, locality, a-causality, rank of the state, maximally chaotic state, maximally entangled state, information...
The Picture Book of Quantum Mechanics
Brandt, Siegmund
2012-01-01
The aim of this book is to explain the basic concepts and phenomena of quantum mechanics by means of visualization. Computer-generated illustrations in color are used extensively throughout the text, helping to establish the relation between quantum mechanics—wave functions, interference, atomic structure, and so forth—and classical physics—point mechanics, statistical mechanics, and wave optics. Even more important, by studying the pictures in parallel with the text, readers develop an intuition for such notoriously abstract phenomena as • the tunnel effect • excitation and decay of metastable states • wave-packet motion within a well • systems of distinguishable and indistinguishable particles • free wave packets and scattering in 3 dimensions • angular-momentum decomposition • stationary bound states in various 3-dimensional potentials • hybrid states • Kepler motion of wave packets in the Coulomb field • spin and magnetic resonance Illustrations from experiments in a variety of f...