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Sample records for schroedinger picture

  1. Abelian Higgs mechanism in the Schroedinger picture

    International Nuclear Information System (INIS)

    Kim, S.K.; Namgung, W.; Soh, K.S.; Yee, J.H.

    1990-01-01

    We have studied symmetry-breaking phenomena in scalar electrodynamics by evaluating the effective potential at one-loop order in the Schroedinger picture. Contributions to the effective potential by the Higgs particle and the transverse and longitudinal components of a photon are compared with other previous works, and they are found to be consistent

  2. Quantum field theory in flat Robertson-Walker space-time functional Schroedinger picture

    International Nuclear Information System (INIS)

    Pi, S.Y.

    1989-01-01

    Quantum field theory in Robertson-Walker space-time is intrinsically time-dependent and the functional Schroedinger picture provides a useful description. We discuss free and self-interacting bosonic quantum field theories: Schroedinger picture quantization, time-dependent Gaussian approximations based on variational principles describing time evolution of pure and mixed states, and renormalizability of the Schroedinger picture. The techniques introduced can be used to study various dynamical questions in early universe processes. (author)

  3. Global spacetime symmetries in the functional Schroedinger picture

    International Nuclear Information System (INIS)

    Halliwell, J.J.

    1991-01-01

    In the conventional functional Schroedinger quantization of field theory, the background spacetime manifold is foliated into a set of three-surfaces and the quantum state of the field is represented by a wave functional of the field configurations on each three-surface. Although this procedure may be covariantly described, the wave functionals generally fail to carry a representation of the complete spacetime symmetry group of the background, such as the Poincare group in Minkowski spacetime, because spacetime symmetries generally involve distortions or motions of the three-surfaces themselves within that spacetime. In this paper, we show that global spacetime symmetries in the functional Schroedinger picture may be represented by parametrizing the field theory---raising to the status of dynamical variables the embedding variables describing the spacetime location of each three-surface. In particular, we show that the embedding variables provide a connection between the purely geometrical operation of an isometry group on the spacetime and the operation of the usual global symmetry generators (constructed from the energy-momentum tensor) on the wave functionals of the theory. We study the path-integral representation of the wave functionals of the parametrized field theory. We show how to construct, from the path integral, wave functionals that are annihilated by the global symmetry generators, i.e., that are invariant under global spacetime symmetry groups. The invariance of the class of histories summed over in the path integral is identified as the source of the invariance of the wave functionals. We apply this understanding to a study of vacuum states in the de Sitter spacetime. We make mathematically precise a previously given heuristic argument for the de Sitter invariance of the matter wave functionals defined by the no-boundary proposal of Hartle and Hawking

  4. Canonical quantization of non-abelian gauge theory in the Schroedinger picture: applications to monopoles and instantons

    International Nuclear Information System (INIS)

    Wadia, S.R.

    1979-01-01

    A detailed formulation of the quantum theory of non-abelian gauge fields is presented in the Schroedinger picture. It is applied to the semiclassical quantization of the t'Hoft-Polyakov monopole, with special attention paid to the treatment of boundary conditions and local and global gauge symmetry. The perturbation expansion is then discussed with the aid of standard collective co-ordinates. In the Prasad-Sommerfield limit, all the eigenfunctions of the fluctuation equation are presented, the ground-state wave function is constructed in terms of gauge and translation invariant co-ordinates, and its total angular momentum is computed to be zero. Aspects of instanton phenomena are then examined in the Schroedinger picture; the role of euclidean time is elucidated. The precise relation between boundary conditions, choice of gauge, and the corresponding picture of the semiclassical vacuum is demonstrated

  5. Erwin Schroedinger

    International Nuclear Information System (INIS)

    Hoffmann, D.

    1984-01-01

    Erwin Schroedinger (1887-1961) belongs without doubt to the most outstanding physicists of our century. His name is inseparably connected with the development of quantum theory with the formulation of his famous wave equation being his greatest achievement. This relation became generally known as the Schroedinger equation and its understanding was fundamental to the progress of modern quantum theory. In 1933 Schroedinger's work was honoured by the award of the Nobel Prize in physics. In the booklet Schroedinger's life, work and philosophical views are outlined against the social and physico-historical background of his time

  6. Schroedinger fluid

    International Nuclear Information System (INIS)

    Kan, K.K.

    1983-01-01

    The relationship of nuclear internal flow and collective inertia, the difference of this flow from that of a classical fluid, and the approach of this flow to rigid flow in independent-particle model rotation are elucidated by reviewing the theory of Schroedinger fluid and its implications for collective vibration and rotation. (author)

  7. Schroedinger's cat

    Energy Technology Data Exchange (ETDEWEB)

    Lubkin, E [Wisconsin Univ., Madison (USA). Dept. of Physics

    1979-08-01

    The issue is to seek quantum interference effects in an arbitrary field, in particular in psychology. For this a digest of quantum mechanics over finite-n-dimensional Hilbert space is invented. In order to match crude data not only von Neumann's mixed states are used but also a parallel notion of unsharp tests. The mathematically styled text (and earlier work on multibin tests, designated MB) deals largely with these new tests. Quantum psychology itself is only given a foundation. It readily engenders objections; its plausibility is developed gradually, in interlocking essays. There is also the empirically definite proposal that (state, test, outcome)-indexed counts be gathered to record data, then fed to a matrix format (MF) search for quantum models. A previously proposed experiment in visual perception which has since failed to find significant quantum correlations, is discussed. The suspicion that quantum mechanics is all around goes beyond MF, and Schroedinger's cat symbolizes this broader perspective.

  8. Schroedinger's cat

    International Nuclear Information System (INIS)

    Lubkin, E.

    1979-01-01

    The issue is to seek quantum interference effects in an arbitrary field, in particular in psychology. For this a digest of quantum mechanics over finite-n-dimensional Hilbert space is invented. In order to match crude data not only von Neumann's mixed states are used but also a parallel notion of unsharp tests. The mathematically styled text (and earlier work on multibin tests, designated MB) deals largely with these new tests. Quantum psychology itself is only given a foundation. It readily engenders objections; its plausibility is developed gradually, in interlocking essays. There is also the empirically definite proposal that (state, test, outcome)-indexed counts be gathered to record data, then fed to a 'matrix format' (MF) search for quantum models. A previously proposed experiment in visual perception which has since failed to find significant quantum correlations, is discussed. The suspicion that quantum mechanics is all around goes beyond MF, and 'Schroedinger's cat' symbolizes this broader perspective. (author)

  9. The Schroedinger operator as a generalized Laplacian

    International Nuclear Information System (INIS)

    Grabowska, Katarzyna; Urbanski, Pawel; Grabowski, Janusz

    2008-01-01

    The Schroedinger operators on the Newtonian spacetime are defined in a way which make them independent of the class of inertial observers. In this picture the Schroedinger operators act not on functions on the spacetime but on sections of a certain one-dimensional complex vector bundle-the Schroedinger line bundle. This line bundle has trivializations indexed by inertial observers and is associated with an U(1)-principal bundle with an analogous list of trivializations-the Schroedinger principal bundle. If an inertial frame is fixed, the Schroedinger bundle can be identified with the trivial bundle over spacetime, but as there is no canonical trivialization (inertial frame), these sections interpreted as 'wavefunctions' cannot be viewed as actual functions on the spacetime. In this approach, the change of an observer results not only in the change of actual coordinates in the spacetime but also in a change of the phase of wavefunctions. For the Schroedinger principal bundle, a natural differential calculus for 'wave forms' is developed that leads to a natural generalization of the concept of the Laplace-Beltrami operator associated with a pseudo-Riemannian metric. The free Schroedinger operator turns out to be the Laplace-Beltrami operator associated with a naturally distinguished invariant pseudo-Riemannian metric on the Schroedinger principal bundle. The presented framework does not involve any ad hoc or axiomatically introduced geometrical structures. It is based on the traditional understanding of the Schroedinger operator in a given reference frame-which is supported by producing right physics predictions-and it is proven to be strictly related to the frame-independent formulation of analytical Newtonian mechanics and Hamilton-Jacobi equations that makes a bridge between the classical and quantum theory

  10. Fractional Schroedinger equation

    International Nuclear Information System (INIS)

    Laskin, Nick

    2002-01-01

    Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

  11. The paradox of Schroedinger's waves

    International Nuclear Information System (INIS)

    Gribben, John.

    1987-01-01

    The paper examines the contribution of the work of Erwin Schroedinger in quantum physics. The Schroedinger equation was developed to explain the behavior of electrons within an atom in terms of waves, and it has proved one of the most useful tools in quantum physics. The Schroedinger 'Cat' experiment is also described and discussed. Finally Schroedinger's ideas on chromosomes in molecular biology are briefly outlined. (U.K.)

  12. Crystallized Schroedinger cat states

    International Nuclear Information System (INIS)

    Castanos, O.; Lopez-Pena, R.; Man'ko, V.I.

    1995-01-01

    Crystallized Schroedinger cat states (male and female) are introduced on the base of extension of group construction for the even and odd coherent states of the electromagnetic field oscillator. The Wigner and Q functions are calculated and some are plotted for C 2 , C 3 , C 4 , C 5 , C 3v Schroedinger cat states. Quadrature means and dispersions for these states are calculated and squeezing and correlation phenomena are studied. Photon distribution functions for these states are given explicitly and are plotted for several examples. A strong oscillatory behavior of the photon distribution function for some field amplitudes is found in the new type of states

  13. Almost periodic Schroedinger operators

    International Nuclear Information System (INIS)

    Bellissard, J.; Lima, R.

    1984-01-01

    These lectures are devoted to recent developments in the theory of almost-periodic Schroedinger Operators. We specially describe the algebraic point of view, with applications to gap-labelling theorems. Particular models are also presented which exhibit various spectral properties. (orig.)

  14. The forced nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Kaup, D.J.; Hansen, P.J.

    1985-01-01

    The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

  15. Philosophy of Erwin Schroedinger: a diachronic view of Schroedinger's thoughts

    International Nuclear Information System (INIS)

    Melgar, M.F.

    1988-01-01

    There is no agreement within the scientific community about the philosophy of Schroedinger. Some people think that he was a realist, while others defend him as an idealist. In this paper we study a number of Schroedinger's works and we show that the epithets of realist and idealist do not do him justice. Toward the end we conclude that it would be more adequate to place him in the trend known as the philosophy of immanence

  16. Properties of squeezed Schroedinger cats

    International Nuclear Information System (INIS)

    Obada, A.S.F.; Omar, Z.M.

    1995-09-01

    In this article we investigate some statistical properties of the even and odd squeezed (squeezed Schroedinger cat) states. The quasi-probability distribution functions especially W(α) and Q(α) are calculated and discussed for these states. The phase distribution function is discussed. A generation scheme is proposed for either the squeezed generalized Schroedinger cat, or the squeezed number state. (author). 35 refs, 5 figs

  17. The Schroedinger problem

    International Nuclear Information System (INIS)

    Da Costa, N.C.A.; Krause, D.; French, S.

    1992-01-01

    Schroedinger introduced discussions about the inconsistency between the classical conception of particles as individual entities and the way in which modern physics treats such particles. In particular, it is noted that quantal particles apparently appear to lack individuality, and that certain suppositions of quantum theory imply that permutations of 'identical' particles are not regarded as observable, hence implying that they must be taken as 'non-individuals' of some kind. An overview is presented in this paper of some results obtained by the authors in the field of non-reflexive logics, which have some bearings on these problems and which can perhaps provide an adequate mathematical tool for dealing with some of the fundamental features of elementary particles, such as for instance the fact that identity apparently lacks sense with respect to them, that particle permutations are not regarded as observable and that a collection of these entities cannot be considered as a set in the sense of the usual theories of sets. The main objective of the paper is to show that the nature of elementary particles can be described in terms of certain non-classical logics, despite the problems regarding their individuality. (authors). 28 refs

  18. A life of Erwin Schroedinger; Erwin Schroedinger. Eine Biographie

    Energy Technology Data Exchange (ETDEWEB)

    Moore, Walter J.

    2012-07-01

    Erwin Schroedinger (1887-1961) was a pioneer of quantum physics, one of the most important scientists of the 20th century at all and - a charming Austrian. He was a man with a passionate interest in people and ideas. Mostly known he became by his representation of quantum theory in the form of wave mechanics, for which he got the Nobel prize for physics and naturally by the famous thought experiment ''Schroedinger's cat''. Walter Moore's biography is very close to the person of Schroedinger and presents his scientific work in the context of his private friendships, his interest in mysticism, and in front of the moving background of the political events in Germany and Austria.

  19. Schroedinger's variational method of quantization revisited

    International Nuclear Information System (INIS)

    Yasue, K.

    1980-01-01

    Schroedinger's original quantization procedure is revisited in the light of Nelson's stochastic framework of quantum mechanics. It is clarified why Schroedinger's proposal of a variational problem led us to a true description of quantum mechanics. (orig.)

  20. A life of Erwin Schroedinger

    International Nuclear Information System (INIS)

    Moore, Walter J.

    2012-01-01

    Erwin Schroedinger (1887-1961) was a pioneer of quantum physics, one of the most important scientists of the 20th century at all and - a charming Austrian. He was a man with a passionate interest in people and ideas. Mostly known he became by his representation of quantum theory in the form of wave mechanics, for which he got the Nobel prize for physics and naturally by the famous thought experiment ''Schroedinger's cat''. Walter Moore's biography is very close to the person of Schroedinger and presents his scientific work in the context of his private friendships, his interest in mysticism, and in front of the moving background of the political events in Germany and Austria.

  1. Schroedinger and the wave mechanics

    International Nuclear Information System (INIS)

    Bassalo, J.M.F.

    1987-01-01

    In commemoration of the centennial of Schroedinger's birth, in 1987, we show in this paper some aspects of his academic life, and his philosophical and scientific work. Among Schroedinger's innumerable contributions to almost all areas of philosophy and science, we choose here the creation of quantum mechanics (1926), considered one of the pillars of Modern quantum theory, and the importance of his philosophical essay What is life (1944). This publication was responsible for a great in the studies of biology, culminating in the discovery of the DNA molecular structure, in 1953, by Crick and Watson, thanks to the X-rays diffraction technique of the DNA developed by Wilkens. (author) [pt

  2. Heisenberg picture and measurement operation

    International Nuclear Information System (INIS)

    D'Espagnat, B.

    1992-01-01

    The idea is discussed according to which, in the Heisenberg picture, differently from the Schroedinger picture, the operators correspond exactly to the dynamic properties and the role of the density matrix is merely to describe our passive knowledge thereof. It is shown that the idea in question cannot be consistently kept as it is, and hints are given as to how it could be refined. (from author). 2 refs

  3. Schroedinger operators and evolutionary strategies

    International Nuclear Information System (INIS)

    Asselmeyer, T.

    1997-01-01

    First we introduce a simple model for the description of evolutionary algorithms, which is based on 2nd order partial differential equations for the distribution function of the individuals. Then we turn to the properties of Boltzmann's and Darwin's strategy. the next chapter is dedicated to the mathematical properties of Schroedinger operators. Both statements on the spectral density and their reproducibility during the simulation are summarized. The remaining of this chapter are dedicated to the analysis of the kernel as well as the dependence of the Schroedinger operator on the potential. As conclusion from the results of this chapter we obtain the classification of the strategies in dependence of the fitness. We obtain the classification of the evolutionary strategies, which are described by a 2nd order partial differential equation, in relation to their solution behaviour. Thereafter we are employed with the variation of the mutation distribution

  4. Correspondence passed between Einstein and Schroedinger

    International Nuclear Information System (INIS)

    Balibar, F.

    1992-01-01

    The main points of the 26 year long correspondence between Einstein and Schroedinger are reviewed: from the de Broglie thesis and the Bose-Einstein statistics to the Schroedinger equation (1925-1926); from the EPR paradox to the cat parable (1935); a complete collaboration on unitary theories

  5. P-adic Schroedinger type equation

    International Nuclear Information System (INIS)

    Vladimirov, V.S.; Volovich, I.V.

    1988-12-01

    In p-adic quantum mechanics a Schroedinger type equation is considered. We discuss the appropriate notion of differential operators. A solution of the Schroedinger type equation is given. A new set of vacuum states for the p-adic quantum harmonic oscillator is presented. The correspondence principle with the standard quantum mechanics is discussed. (orig.)

  6. In search of Schroedinger's cat

    International Nuclear Information System (INIS)

    Gribbin, John.

    1984-01-01

    The book explains how the paradox of Schroedinger's cat led to an understanding of reality in quantum physics. The contents of the book is divided into three parts. Part one concerns light, atoms and Bohr's atom. Quantum mechanics is discussed in Part Two, including photons and electrons, matrices and waves, and applications of quanta. The last part deals with chance and uncertainty, paradoxes and possibilities, the experimental proof of the paradoxical reality of the quantum world, and the many-worlds interpretation of quantum mechanics. (U.K.)

  7. Introduction to Schroedinger inverse scattering

    International Nuclear Information System (INIS)

    Roberts, T.M.

    1991-01-01

    Schroedinger inverse scattering uses scattering coefficients and bound state data to compute underlying potentials. Inverse scattering has been studied extensively for isolated potentials q(x), which tend to zero as vertical strokexvertical stroke→∞. Inverse scattering for isolated impurities in backgrounds p(x) that are periodic, are Heaviside steps, are constant for x>0 and periodic for x<0, or that tend to zero as x→∞ and tend to ∞ as x→-∞, have also been studied. This paper identifies literature for the five inverse problems just mentioned, and for four other inverse problems. Heaviside-step backgrounds are discussed at length. (orig.)

  8. Effective Schroedinger equations on submanifolds

    Energy Technology Data Exchange (ETDEWEB)

    Wachsmuth, Jakob

    2010-02-11

    In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.

  9. Some threshold spectral problems of Schroedinger operators

    International Nuclear Information System (INIS)

    Jia, X.

    2009-01-01

    This Ph.D. thesis deals with some spectral problems of the Schroedinger operators. We first consider the semi-classical limit of the number of bound states of unique two-cluster N-body Schroedinger operator. Then we use Dirichlet-Neumann bracket to get semi-classical limit of Riesz means of the discrete eigenvalues of N-body Schroedinger operator. The effective potential of N-body Schroedinger operator with Coulomb potential is also considered and we find that the effective potential has critical decay at infinity. Thus, the Schroedinger operator with critical potential is studied in this thesis. We study the coupling constant threshold of Schroedinger operator with critical potential and the asymptotic expansion of resolvent of Schroedinger operator with critical potential. We use that expansion to study low-energy asymptotics of derivative of spectral shift function for perturbation with critical decay. After that, we use this result and the known result for high-energy asymptotic expansion of spectral shift function to obtain the Levinson theorem. (author)

  10. Schroedinger representation in quantum field theory

    International Nuclear Information System (INIS)

    Luescher, M.

    1985-01-01

    Until recently, the Schroedinger representation in quantum field theory had not received much attention, even more so because there were reasons to believe that in the presence of interactions it did not exist in a mathematically well-defined sense. When Symanzik set out to solve this problem, he was motivated by a special 2-dimensional case, the relativistic string model, in which the Schroedinger wave functionals are the primary objects of physical interest. Also, he knew that if it were possible to demonstrate the existence of the Schroedinger representation, the (then unproven) ultraviolet finiteness of the Casimir force in renormalizable quantum field theories would probably follow. (orig./HSI)

  11. Erwin Schroedinger, Francis Crick and epigenetic stability

    Directory of Open Access Journals (Sweden)

    Ogryzko Vasily V

    2008-04-01

    Full Text Available Abstract Schroedinger's book 'What is Life?' is widely credited for having played a crucial role in development of molecular and cellular biology. My essay revisits the issues raised by this book from the modern perspective of epigenetics and systems biology. I contrast two classes of potential mechanisms of epigenetic stability: 'epigenetic templating' and 'systems biology' approaches, and consider them from the point of view expressed by Schroedinger. I also discuss how quantum entanglement, a nonclassical feature of quantum mechanics, can help to address the 'problem of small numbers' that led Schroedinger to promote the idea of a molecular code-script for explaining the stability of biological order.

  12. Erwin Schroedinger, Francis Crick and epigenetic stability.

    Science.gov (United States)

    Ogryzko, Vasily V

    2008-04-17

    Schroedinger's book 'What is Life?' is widely credited for having played a crucial role in development of molecular and cellular biology. My essay revisits the issues raised by this book from the modern perspective of epigenetics and systems biology. I contrast two classes of potential mechanisms of epigenetic stability: 'epigenetic templating' and 'systems biology' approaches, and consider them from the point of view expressed by Schroedinger. I also discuss how quantum entanglement, a nonclassical feature of quantum mechanics, can help to address the 'problem of small numbers' that led Schroedinger to promote the idea of a molecular code-script for explaining the stability of biological order.

  13. Reparametrization invariance and the Schroedinger equation

    International Nuclear Information System (INIS)

    Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.

    1999-01-01

    A time-dependent Schroedinger equation for systems invariant under the reparametrization of time is considered. We develop the two-stage procedure of construction such systems from a given initial ones, which are not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schroedinger equation. The procedure is applicable in the supersymmetric theories as well. The n = 2 supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schroedinger equation

  14. Stochastic effects on the nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Flessas, G P; Leach, P G L; Yannacopoulos, A N

    2004-01-01

    The aim of this article is to provide a brief review of recent advances in the field of stochastic effects on the nonlinear Schroedinger equation. The article reviews rigorous and perturbative results. (review article)

  15. Simulation of the Schroedinger equation on SHAC

    International Nuclear Information System (INIS)

    Stewart, A.

    1976-01-01

    A simulation of the Schroedinger wave equation for the hydrogen atom, on SHAC, a simple homogeneous analogue computer primarily intended for use in schools, is described. Due to the incorporation of FET switches very high speed switching from initial conditions to compute modes is possible. The techniques employed in the multiplier and divider are discussed and the flow diagram for the Schroedinger program shown. Results and photographs are discussed. (U.K.)

  16. The phase space of the focused cubic Schroedinger equation: A numerical study

    Energy Technology Data Exchange (ETDEWEB)

    Burlakov, Yuri O. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

    1998-05-01

    distinctly different components. They point out the interesting fact that the phase space into distinctly different components. They point out the interesting fact that the phase transition type behavior of the discretized cubic Schroedinger equation can be observed in a discretization with as few as 2 points. The refinement of the discretization does not change the global picture qualitatively. The authors vary two parameters in the canonical ensemble of the cubic Schroedinger equation: the first parameter is the temperature, the second one is a certain constraint on the function space. They demonstrate that at a fixed low temperature, as the constraint varies, the canonical ensemble of the cubic Schroedinger equation undergoes a bifurcation which is manifested both in the change in the shape of the typical function and in a corresponding change of the structure of the phase space.

  17. Correspondence passed between Einstein and Schroedinger; La correspondance entre Einstein et Schroedinger

    Energy Technology Data Exchange (ETDEWEB)

    Balibar, F. [Paris-7 Univ., 75 (France)

    1992-12-31

    The main points of the 26 year long correspondence between Einstein and Schroedinger are reviewed: from the de Broglie thesis and the Bose-Einstein statistics to the Schroedinger equation (1925-1926); from the EPR paradox to the cat parable (1935); a complete collaboration on unitary theories.

  18. Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation

    International Nuclear Information System (INIS)

    Ren Ji; Ruan Hangyu

    2008-01-01

    We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained

  19. Nonrelativistic Schroedinger equation in quasi-classical theory

    International Nuclear Information System (INIS)

    Wignall, J.W.G.

    1987-01-01

    The author has recently proposed a quasi-classical theory of particles and interactions in which particles are pictured as extended periodic disturbances in a universal field chi(x,t), interacting with each other via nonlinearity in the equation of motion for chi. The present paper explores the relationship of this theory to nonrelativistic quantum mechanics; as a first step, it is shown how it is possible to construct from chi a configuration-space wave function Psi(x 1 , X 2 , t), and that the theory requires that Psi satisfy the two-particle Schroedinger equation in the case where the two particles are well separated from each other. This suggests that the multiparticle Schroedinger equation can be obtained as a direct consequence of the quasi-classical theory without any use of the usual formalism (Hilbert space, quantization rules, etc.) of conventional quantum theory and in particular without using the classical canonical treatment of a system as a crutch theory which has subsequently to be quantized. The quasi-classical theory also suggests the existence of a preferred absolute gauge for the electromagnetic potentials

  20. Some studies of Schroedinger operators

    International Nuclear Information System (INIS)

    Liu Yang.

    1993-09-01

    This thesis consists of three papers. Paper 1 deals with the semiclassical approximation for a Schroedinger operator in one dimension with an arbitrary continuous potential. The basic result is that function in the range of a spectral projection associated with an interval are exponentially small (with respect to Plancks parameter h) in places where the potential exceeds the interval. As an application of this result, it is shown that the eigenvalues of the operator localized to the wells appear as resonances of the global operator. This is true also when the potential is not bounded from below. Such results were proved before for analytic potentials by analytic dilatation. In Paper 2, the potential is assumed to have the form of χ + V(χ) (the Stark Hamiltonian) with a well-behaved V(χ), an explicit spectral and scattering theory for such an operator was presented using the time-independent approach. In particular, we derive an eigenfunction expansion theorem which, combined with a construction of an intertwining operator, gives a solution of the inverse scattering problem according to L. Daddeev and A. Melin. The direct part of the second paper has a generalization to higher dimensions, and this was done in the third paper. Also in that paper, the condition on the potentials for doing the inverse scattering theory was relaxed, and an explicit formula for the potentials involving the first approximation of the scattering data was given

  1. The Schroedinger and Dirac free particle equations without quantum mechanics

    International Nuclear Information System (INIS)

    Ord, G.N.

    1996-01-01

    Einstein close-quote s theory of Brownian Movement has provided a well accepted microscopic model of diffusion for many years. Until recently the relationship between this model and Quantum Mechanics has been completely formal. Brownian motion provides a microscopic model for diffusion, but quantum mechanics and diffusion are related by a formal analytic continuation, so the relationship between Brownian motion and Quantum Mechanics has been correspondingly vague. Some recent work has changed this picture somewhat and here we show that a random walk model of Brownian motion produces the diffusion equation or the telegraph equations as a descriptions of particle densities, while at the same time the correlations in the space-time geometry of these same Brownian particles obey the Schroedinger and Dirac equations respectively. This is of interest because the equations of Quantum Mechanics appear here naturally in a classical context without the problems of interpretation they have in the usual context. copyright 1996 Academic Press, Inc

  2. On the connection between Schroedinger- and Dirichlet forms

    International Nuclear Information System (INIS)

    Albeverio, S.; Bochum Univ.; Gesztesy, F.; Karwowski, W.; Streit, L.; Bielefeld Univ.

    Relations between Schroedinger forms associated with Schroedinger operators in L 2 (Ω;dsup(n)x), Ω is contained in Rsup(n) open, n >= 1 and the corresponding Dirichlet forms are investigated. Various concrete examples are presented. (orig.)

  3. Unifying quanta and relativity. Schroedinger`s attitude to relativistic quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Kragh, H. [Roskilde Universitetscenter (Denmark)

    1992-12-31

    A considerable part of Schroedinger`s scientific work focused on the relationship between quantum theory and the theory of relativity. This paper provides a historical analysis of his occupation on this subject in the period 1925-1934. The first section surveys the role played by relativity in Schroedinger`s formation of wave mechanics in 1925-1926; the second section analyzes his attempt to make sense of Dirac`s theory of the electron by proposing a relativistic wave equation with positive energies only. In this work, which took place in 1930-1931, Schroedinger discovered the Zitterbewegung that Dirac electrons will exhibit even in a field-free case. Schroedinger`s failed attempt to introduce an alternative to the Dirac theory was part of his general dissatisfaction with the current state of quantum mechanics. It is argued that, to a large extent, his work on the Dirac theory was philosophically motivated and that it contributed to his alienation from mainstream quantum physics in the 1930s. (author). 54 refs.

  4. Single-particle Schroedinger fluid. I. Formulation

    International Nuclear Information System (INIS)

    Kan, K.K.; Griffin, J.J.

    1976-01-01

    The problem of a single quantal particle moving in a time-dependent external potential well is formulated specifically to emphasize and develop the fluid dynamical aspects of the matter flow. This idealized problem, the single-particle Schroedinger fluid, is shown to exhibit already a remarkably rich variety of fluid dynamical features, including compressible flow and line vortices. It provides also a sufficient framework to encompass simultaneously various simplified fluidic models for nuclei which have earlier been postulated on an ad hoc basis, and to illuminate their underlying restrictions. Explicit solutions of the single-particle Schroedinger fluid problem are studied in the adiabatic limit for their mathematical and physical implications (especially regarding the collective kinetic energy). The basic generalizations for extension of the treatment to the many-body Schroedinger fluid are set forth

  5. A life of Erwin Schroedinger. 2. ed.

    International Nuclear Information System (INIS)

    Moore, Walter J.

    2015-01-01

    Erwin Schroedinger (1887-1961) was a pioneer of quantum physics, one of the most important scientist of the 20th century at all and a charming Austrian. He was a man with a passionate interest for men and ideas. Mostly known he became by his representation of quantum theory in the form of wave mechanics, for which he obtained the Nobel prize for physics and naturally by the famous thought experiment ''Schroedingers cat''. Walter Moore's biography is quite near to the person of Schroedinger and presents his scientific work in the context of his friendships, his interset for mysticism, and in front of the moving background of the political events in Germany and Austria.

  6. Some physical applications of fractional Schroedinger equation

    International Nuclear Information System (INIS)

    Guo Xiaoyi; Xu Mingyu

    2006-01-01

    The fractional Schroedinger equation is solved for a free particle and for an infinite square potential well. The fundamental solution of the Cauchy problem for a free particle, the energy levels and the normalized wave functions of a particle in a potential well are obtained. In the barrier penetration problem, the reflection coefficient and transmission coefficient of a particle from a rectangular potential wall is determined. In the quantum scattering problem, according to the fractional Schroedinger equation, the Green's function of the Lippmann-Schwinger integral equation is given

  7. Quantum derivatives and the Schroedinger equation

    International Nuclear Information System (INIS)

    Ben Adda, Faycal; Cresson, Jacky

    2004-01-01

    We define a scale derivative for non-differentiable functions. It is constructed via quantum derivatives which take into account non-differentiability and the existence of a minimal resolution for mean representation. This justify heuristic computations made by Nottale in scale-relativity. In particular, the Schroedinger equation is derived via the scale-relativity principle and Newton's fundamental equation of dynamics

  8. A reliable treatment for nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Khani, F.; Hamedi-Nezhad, S.; Molabahrami, A.

    2007-01-01

    Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schroedinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation

  9. The Universe according to Schroedinger and Milo

    Science.gov (United States)

    Wolff, Milo

    2009-10-01

    The puzzling electron is due to the belief that it is a discrete particle. Schroedinger, (1937) eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). Thus he rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff using a Scalar Wave Equation in 3D quantum space to find wave solutions. The resulting Wave Structure of Matter (WSM) contains all the electron's properties including the Schroedinger Equation. Further, Newton's Law F=ma is no longer a puzzle; It originates from Mach's principle of inertia (1883) that depends on the space medium and the WSM. These the origin of all the Natural Laws. Carver Mead (1999) at CalTech used the WSM to design Intel micro-chips and to correct errors of Maxwell's Equations. Applications of the WSM describe matter at molecular dimensions: Industrial alloys, catalysts, biology and medicine, molecular computers and memories. See book ``Schroedinger's Universe'' - at Amazon.com. Pioneers of the WSM are growing rapidly. Some are: SpaceAndMotion.com, QuantumMatter.com, treeincarnation.com/audio/milowolff.htm, daugerresearch.com/orbitals/index.shtml, glafreniere.com/matter.html =A new Universe.

  10. Schroedinger's Wave Structure of Matter (WSM)

    Science.gov (United States)

    Wolff, Milo; Haselhurst, Geoff

    2009-10-01

    The puzzling electron is due to the belief that it is a discrete particle. Einstein deduced this structure was impossible since Nature does not allow the discrete particle. Clifford (1876) rejected discrete matter and suggested structures in `space'. Schroedinger, (1937) also eliminated discrete particles writing: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). He rejected wave-particle duality. Schroedinger's concept was developed by Milo Wolff and Geoff Haselhurst (SpaceAndMotion.com) using the Scalar Wave Equation to find spherical wave solutions in a 3D quantum space. This WSM, the origin of all the Natural Laws, contains all the electron's properties including the Schroedinger Equation. The origin of Newton's Law F=ma is no longer a puzzle; It originates from Mach's principle of inertia (1883) that depends on the space medium and the WSM. Carver Mead (1999) at CalTech used the WSM to design Intel micro-chips correcting errors of Maxwell's magnetic Equations. Applications of the WSM also describe matter at molecular dimensions: alloys, catalysts, biology and medicine, molecular computers and memories. See ``Schroedinger's Universe'' - at Amazon.com

  11. Some spectral equivalences between Schroedinger operators

    International Nuclear Information System (INIS)

    Dunning, C; Hibberd, K E; Links, J

    2008-01-01

    Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schroedinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In this manner we obtain equivalences between PT-symmetric problems and Hermitian problems. We also find equivalences between some classes of Hermitian operators

  12. Spectral problem for the radial Schroedinger equation

    International Nuclear Information System (INIS)

    Vshivtsev, A.S.; Tatarintsev, A.V.; Prokopov, A.V.; Sorokin, V. N.

    1998-01-01

    For the first time, a procedure for determining spectra on the basis of generalized integral transformations is implemented for a wide class of radial Schroedinger equations. It is shown that this procedure works well for known types of potentials. Concurrently, this method makes it possible to obtain new analytic results for the Cornell potential. This may prove important for hadron physics

  13. Bell's theorem and quantum realism. Reassessment in light of the Schroedinger paradox

    International Nuclear Information System (INIS)

    Shakur, Asif M.; Hemmick, Douglas L.

    2012-01-01

    Quantum theory presents a strange picture of the world, offering no real account of physical properties apart from observation. Neils Bohr felt that this reflected a core truth of nature: ''There is no quantum world. There is only an abstract mathematical description.'' Among the most significant developments since Bohr's day has been the theorem of John S. Bell. It is important to consider whether Bell's analysis supports such a denial of microrealism. In this book, we evaluate the situation in terms of an early work of Erwin Schroedinger. Doing so, we see how Bell's theorem is conceptually related to the Conway and Kochen Free Will theorem and also to all the major anti-realism efforts. It is easy to show that none of these analyses imply the impossibility of objective realism. We find that Schroedinger's work leads to the derivation of a new series of theoretical proofs and potential experiments, each involving ''entanglement,'' the link between particles in some quantum systems. (orig.)

  14. Considerations on Bohr's, Heisenberg's and Schroedinger's philosophy

    International Nuclear Information System (INIS)

    Shimony, A.

    1981-01-01

    In denying that the words 'physical reality' are meaningful without reference to an experimental arrangement, Bohr renounces any knowledge of the 'thing-in-itself'. However, the relation of his epistemology to both idealism and positivism remains obscure. Heisenberg departs from Bohr in enunciating a metaphysical implication of quantum mechanics. Heisenberg asserts that there is an intermediate modality -potentiality- between logical possibility and existence. His attempts to explain the transition from potentiality to existence are not convincing. Schroedinger rejects Bohr's interpretation of quantum mechanics as a positivist exercise and seeks instead a realist interpretation. Nevertheless, the metaphysics of Schroedinger is fundamentally idealistic, maintaining that the material aspect of the world is composed of the same elements as mind, but in a different order [fr

  15. Schroedinger and the interpretation of quantum mechanics

    International Nuclear Information System (INIS)

    Rohrlich, F.

    1987-01-01

    On the occasion of the centennial of his birth, Schroedinger's life and views are sketched and his critique of the interpretation of quantum mechanics accepted at his time is examined. His own interpretation, which he had to abandon after a short time, provides a prime example of the way in which the tentative meaning of central theoretical terms in a new and revolutionary theory often fails. Schroedinger's strong philosophical convictions have played a key role in his refusal to break with many of the notions of classical physics. At the same time, they made him into a keen and incisive critic of the Copenhagen interpretation. His criticism is compared with present views on quantum mechanics

  16. Measurement theory and the Schroedinger equation

    International Nuclear Information System (INIS)

    Schwarz, A.S.; Tyupkin, Yu.S.

    1987-01-01

    The paper is an analysis of the measuring process in quantum mechanics based on the Schroedinger equation. The arguments employed use an assumption reflecting, to some extent, the statistical properties of the vacuum. A description is given of the cases in which different incoherent superpositions of pure states in quantum mechanics are physically equivalent. The fundamental difference between quantum and classical mechanics as explained by the existence of unobservable variables is discussed. (U.K.)

  17. Exchange effects in Relativistic Schroedinger Theory

    International Nuclear Information System (INIS)

    Sigg, T.; Sorg, M.

    1998-01-01

    The Relativistic Schroedinger Theory predicts the occurrence of exchange and overlap effects in many-particle systems. For a 2-particle system, the interaction energy of the two particles consists of two contributions: Coulomb energy and exchange energy, where the first one is revealed to be the same as in standard quantum theory. However the exchange energy is mediated by an exchange potential, contrary to the kinematical origin of the exchange term in the standard theory

  18. Schroedinger covariance states in anisotropic waveguides

    International Nuclear Information System (INIS)

    Angelow, A.; Trifonov, D.

    1995-03-01

    In this paper Squeezed and Covariance States based on Schroedinger inequality and their connection with other nonclassical states are considered for particular case of anisotropic waveguide in LiNiO 3 . Here, the problem of photon creation and generation of squeezed and Schroedinger covariance states in optical waveguides is solved in two steps: 1. Quantization of electromagnetic field is provided in the presence of dielectric waveguide using normal-mode expansion. The photon creation and annihilation operators are introduced, expanding the solution A-vector(r-vector,t) in a series in terms of the Sturm - Liouville mode-functions. 2. In terms of these operators the Hamiltonian of the field in a nonlinear waveguide is derived. For such Hamiltonian we construct the covariance states as stable (with nonzero covariance), which minimize the Schroedinger uncertainty relation. The evolutions of the three second momenta of q-circumflex j and p-circumflex j are calculated. For this Hamiltonian all three momenta are expressed in terms of one real parameters s only. It is found out how covariance, via this parameter s, depends on the waveguide profile n(x,y), on the mode-distributions u-vector j (x,y), and on the waveguide phase mismatching Δβ. (author). 37 refs

  19. The Schroedinger equation and canonical perturbation theory

    International Nuclear Information System (INIS)

    Graffi, S.; Paul, T.

    1987-01-01

    Let T 0 (ℎ,ω)+εV be the Schroedinger operator corresponding to the classical Hamiltonian H 0 (ω)+εV, where H 0 (ω) is the d-dimensional harmonic oscillator with non-resonant frequencies ω=(ω 1 ..., ω d ) and the potential V(q 1 , ..., q d ) is an entire function of order (d+l) -1 . We prove that the algorithm of classical, canonical perturbation theory can be applied to the Schroedinger equation in the Bargmann representation. As a consequence, each term of the Rayleigh-Schroedinger series near any eigenvalue of T 0 (ℎ,ω) admits a convergent expansion in powers of ℎ of initial point the corresponding term of the classical Birkhoff expansion. Moreover if V is an even polynomial, the above result and the KAM theorem show that all eigenvalues λ n (ℎ,ε) of T 0 +εV such that nℎ coincides with a KAM torus are given, up to order ε ∞ , by a quantization formula which reduces to the Bohr-Sommerfeld one up to first order terms in ℎ. (orig.)

  20. A life of Erwin Schroedinger. 2. ed.; Erwin Schroedinger. Eine Biographie

    Energy Technology Data Exchange (ETDEWEB)

    Moore, Walter J.

    2015-07-01

    Erwin Schroedinger (1887-1961) was a pioneer of quantum physics, one of the most important scientist of the 20th century at all and a charming Austrian. He was a man with a passionate interest for men and ideas. Mostly known he became by his representation of quantum theory in the form of wave mechanics, for which he obtained the Nobel prize for physics and naturally by the famous thought experiment ''Schroedingers cat''. Walter Moore's biography is quite near to the person of Schroedinger and presents his scientific work in the context of his friendships, his interset for mysticism, and in front of the moving background of the political events in Germany and Austria.

  1. An implicit spectral formula for generalized linear Schroedinger equations

    International Nuclear Information System (INIS)

    Schulze-Halberg, A.; Garcia-Ravelo, J.; Pena Gil, Jose Juan

    2009-01-01

    We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schroedinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schroedinger equation or the Schroedinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form. (author)

  2. Erwin Schroedinger: Collected papers V. 4. General scientific and popular papers

    International Nuclear Information System (INIS)

    Schroedinger, E.

    1984-01-01

    The present volume contains all of Schroedinger's papers, which did not fit naturally into his earlier volumes. It certainly does not contain only popular writings and is perhaps more so than the other volumes a testimony of the spiritual breadth of its author. Schroedinger occupied himself very extensively with the physiological optics. His papers reach from survey articles, where an enormous experimental material is being sifted, to theoretical explorations. A leitmotiv in Schroedinger's thinking, which never left him in peace, was the duality of particle and wave. He looked upon the wave-picture as the one more to the point and in this connection expressed various fruitful thoughts as e.g. that the state of macroscopic bodies would not be eigenstates of the number of particles. He objected against provisional formulations and thus controverted against quantum jumps, which suggest a discontinuous time-development. Schroedinger rejected the radical positivism, which tolerates only directly observable quantities in a theory and he did not look upon the Copenhagen interpretation as the complete solution to the problem. The collection of 59 papers is a goldmine for all pedagogues. Numerous popularizations of Schroedinger's spheres of interest, which go widely beyond his field of exploration prove how simple and clear a topic can be presented. Let it be astronomy or biology, theory of knowledge or Greek mythology, he always discovered the heart of the questions and illustrated it with simple means. He never pretends learning and deepness of thoughts by cryptical remarks and by vague or contradictory formulations. All writings show his way of thinking, which cannot be restricted by authority and objects to any claim of eternal validity. For instance, he analyses various epoche-making arguements of Galileo and finds that his plausible explanation of the tides is wrong. His conceptions on consciousness, free will and human soul are documented in some essays too

  3. Feynman path integral related to stochastic schroedinger equation

    International Nuclear Information System (INIS)

    Belavkin, V.P.; Smolyanov, O.G.

    1998-01-01

    The derivation of the Schroedinger equation describing the continuous measurement process is presented. The representation of the solution of the stochastic Schroedinger equation for continuous measurements is obtained by means of the Feynman path integral. The connection with the heuristic approach to the description of continuous measurements is considered. The connection with the Senon paradox is established [ru

  4. Solving the Schroedinger equation using Smolyak interpolants

    International Nuclear Information System (INIS)

    Avila, Gustavo; Carrington, Tucker Jr.

    2013-01-01

    In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased

  5. Dual Schroedinger Equation as Global Optimization Algorithm

    International Nuclear Information System (INIS)

    Huang Xiaofei; eGain Communications, Mountain View, CA 94043

    2011-01-01

    The dual Schroedinger equation is defined as replacing the imaginary number i by -1 in the original one. This paper shows that the dual equation shares the same stationary states as the original one. Different from the original one, it explicitly defines a dynamic process for a system to evolve from any state to lower energy states and eventually to the lowest one. Its power as a global optimization algorithm might be used by nature for constructing atoms and molecules. It shall be interesting to verify its existence in nature.

  6. Inversion transformation in the Schroedinger equation

    International Nuclear Information System (INIS)

    Demkov, Yu.N.; Semenova, N.V.

    1984-01-01

    Using the inversion with respect to a sphere in the coordinate space, the equivalence between the Schroedinger equations with different potentials is established. It is shown that the zero-energy equation for a spherically symmetric potential is equivalent to the equation with an axially symmetric potential of a special form. The particular exact solutions of the zero-energy problem for the motion of a particle in the field of two Maxwell ''fish-eye'' potentials and potentials with the two Coulomb singularities are found

  7. Mobile localization in nonlinear Schroedinger lattices

    International Nuclear Information System (INIS)

    Gomez-Gardenes, J.; Falo, F.; Floria, L.M.

    2004-01-01

    Using continuation methods from the integrable Ablowitz-Ladik lattice, we have studied the structure of numerically exact mobile discrete breathers in the standard discrete nonlinear Schroedinger equation. We show that, away from that integrable limit, the mobile pulse is dressed by a background of resonant plane waves with wavevectors given by a certain selection rule. This background is seen to be essential for supporting mobile localization in the absence of integrability. We show how the variations of the localized pulse energy during its motion are balanced by the interaction with this background, allowing the localization mobility along the lattice

  8. Scale calculus and the Schroedinger equation

    International Nuclear Information System (INIS)

    Cresson, Jacky

    2003-01-01

    This paper is twofold. In a first part, we extend the classical differential calculus to continuous nondifferentiable functions by developing the notion of scale calculus. The scale calculus is based on a new approach of continuous nondifferentiable functions by constructing a one parameter family of differentiable functions f(t,ε) such that f(t,ε)→f(t) when ε goes to zero. This led to several new notions as representations: fractal functions and ε-differentiability. The basic objects of the scale calculus are left and right quantum operators and the scale operator which generalizes the classical derivative. We then discuss some algebraic properties of these operators. We define a natural bialgebra, called quantum bialgebra, associated with them. Finally, we discuss a convenient geometric object associated with our study. In a second part, we define a first quantization procedure of classical mechanics following the scale relativity theory developed by Nottale. We obtain a nonlinear Schroedinger equation via the classical Newton's equation of dynamics using the scale operator. Under special assumptions we recover the classical Schroedinger equation and we discuss the relevance of these assumptions

  9. Schroedinger operators and evolutionary strategies; Schroedinger-Operatoren und Evolutionaere Strategien

    Energy Technology Data Exchange (ETDEWEB)

    Asselmeyer, T.

    1997-12-22

    First we introduce a simple model for the description of evolutionary algorithms, which is based on 2nd order partial differential equations for the distribution function of the individuals. Then we turn to the properties of Boltzmann's and Darwin's strategy. the next chapter is dedicated to the mathematical properties of Schroedinger operators. Both statements on the spectral density and their reproducibility during the simulation are summarized. The remaining of this chapter are dedicated to the analysis of the kernel as well as the dependence of the Schroedinger operator on the potential. As conclusion from the results of this chapter we obtain the classification of the strategies in dependence of the fitness. We obtain the classification of the evolutionary strategies, which are described by a 2nd order partial differential equation, in relation to their solution behaviour. Thereafter we are employed with the variation of the mutation distribution.

  10. On the Schroedinger equation for the minisuperspace models

    International Nuclear Information System (INIS)

    Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.

    2000-01-01

    We obtain a time-dependent Schroedinger equation for the Friedmann-Robertson-Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necessary to include an additional action invariant under the reparametrization of time. The last one does not change the equations of motion of the system, but changes only the constraint which at the quantum level becomes time-dependent Schroedinger equation. The same procedure is applied to the supersymmetric case and the supersymmetric quantum constraints are obtained, one of them is a square root of the Schroedinger operator

  11. Interaction of Schroedinger electrons and photons

    International Nuclear Information System (INIS)

    Haller, K.; Sohn, R.B.

    1979-01-01

    The effect of transformations carried out on the Hamiltonian for the Schroedinger electron-photon system is studied. These transformations include gauge transformations and certain similarity and ''hybrid'' transformations. The last named involve unitary transformations of either operators or states, but not both. Unitary and hybrid transformation are discussed, which affect the transverse components of the electromagnetic vector potentials and therefore are distinct from gauge transformations. A hybrid transformation is identified which leads to a form of the Hamiltonian that contains no reference to the transverse vector potential and includes electric and magnetic fields as well as nonlocal interactions of charges and currents. The behavior of the scattering matrix under the influence of these hybrid transformations is discussed. Comments are made on two-photon absorption calculations

  12. Formalism and physical interpretation in Schroedinger

    International Nuclear Information System (INIS)

    Paty, M.

    1992-01-01

    The question of the relation between a formalism and its physical interpretation arises not only when theoretical and conceptual systems are reorganized, but in the theoretical elaboration as well. The Schroedinger's work and thought are examined in this paper with this double concern. His work on the mathematical formalism is constantly sustained by a proper physical thought which takes the form of a wave intuition that guarantees him intelligibility. Concerning his interpretation of quantum mechanics, his thought remains characterized, through its evolution, by a w ave image of the world . The way he deals with space-time structure in General Relativity and favours the possibility of a direct interpretation of space-time geometrical quantities, is also studied. (author). 75 refs

  13. Generalized non-linear Schroedinger hierarchy

    International Nuclear Information System (INIS)

    Aratyn, H.; Gomes, J.F.; Zimerman, A.H.

    1994-01-01

    The importance in studying the completely integrable models have became evident in the last years due to the fact that those models present an algebraic structure extremely rich, providing the natural scenery for solitons description. Those models can be described through non-linear differential equations, pseudo-linear operators (Lax formulation), or a matrix formulation. The integrability implies in the existence of a conservation law associated to each of degree of freedom. Each conserved charge Q i can be associated to a Hamiltonian, defining a time evolution related to to a time t i through the Hamilton equation ∂A/∂t i =[A,Q i ]. Particularly, for a two-dimensions field theory, infinite degree of freedom exist, and consequently infinite conservation laws describing the time evolution in space of infinite times. The Hamilton equation defines a hierarchy of models which present a infinite set of conservation laws. This paper studies the generalized non-linear Schroedinger hierarchy

  14. Structural invariance of the Schroedinger equation and chronoprojective geometry

    International Nuclear Information System (INIS)

    Burdet, G.; Perrin, M.

    1983-07-01

    We describe an extension of the chronoprojective geometry and show how its automorphisms are related to the invariance properties of the Schroedinger equation describing a quantum test particle in any Newton-Cartan structure

  15. Monodromy of the matrix Schroedinger equations and Darboux transformations

    CERN Document Server

    Goncharenko, V M

    1998-01-01

    A Schroedinger operator L=-d sup 2 /dz sup 2 +U(z) with a matrix-valued rational potential U(z) is said to have trivial monodromy if all the solutions of the corresponding Schroedinger equations L psi=lambda psi are single-valued in the complex plane z is an element of C for any lambda. A local criterion of this property in terms of the Laurent coefficients of the potential U near its singularities, which are assumed to be regular, is found. It is proved that any such operator with a potential vanishing at infinity can be obtained by a matrix analogue of the Darboux transformation from the Schroedinger operator L sub o =-d sup 2 /dz sup 2. This generalizes the well known Duistermaat-Gruenbaum result to the matrix case and gives the explicit description of the Schroedinger operators with trivial monodromy in this case. (author)

  16. Schroedinger operators - geometric estimates in terms of the occupation time

    International Nuclear Information System (INIS)

    Demuth, M.; Kirsch, W.; McGillivray, I.

    1995-01-01

    The difference of Schroedinger and Dirichlet semigroups is expressed in terms of the Laplace transform of the Brownian motion occupation time. This implies quantitative upper and lower bounds for the operator norms of the corresponding resolvent differences. One spectral theoretical consequence is an estimate for the eigenfunction for a Schroedinger operator in a ball where the potential is given as a cone indicator function. 12 refs

  17. Wigner function and Schroedinger equation in phase-space representation

    International Nuclear Information System (INIS)

    Chruscinski, Dariusz; Mlodawski, Krzysztof

    2005-01-01

    We discuss a family of quasidistributions (s-ordered Wigner functions of Agarwal and Wolf [Phys. Rev. D 2, 2161 (1970); Phys. Rev. D 2, 2187 (1970); Phys. Rev. D 2, 2206 (1970)]) and its connection to the so-called phase space representation of the Schroedinger equation. It turns out that although Wigner functions satisfy the Schroedinger equation in phase space, they have a completely different interpretation

  18. Discrete transparent boundary conditions for Schroedinger-type equations

    International Nuclear Information System (INIS)

    Schmidt, F.; Yevick, D.

    1997-01-01

    We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schroedinger-type equations. Our method supplies boundary conditions for the θ-family of implicit one-step discretizations of Schroedinger's equation in time. The use of Mikusinski's operator approach in time avoids direct and inverse transforms between time and frequency domains and thus implements the boundary conditions in a direct manner. 14 refs., 9 figs

  19. Linearised collective Schroedinger equation for nuclear quadrupole surface vibrations

    International Nuclear Information System (INIS)

    Greiner, M.; Heumann, D.; Scheid, W.

    1990-11-01

    The linearisation of the Schroedinger equation for nuclear quadrupole surface vibrations yields a new spin degree of freedom, which is called collective spin and has a value of 3/2. With the introduction of collective spin dependent potentials, this linearised Schroedinger equation is then used for the description of low energy spectra and electromagnetic transition probabilities of some even-odd Xe, Ir and Au nuclei which have a spin 3/2 in their groundstate. (orig.)

  20. Picture perfect

    DEFF Research Database (Denmark)

    Pless, Mette; Sørensen, Niels Ulrik

    Picture perfect’ – when perfection becomes the new normal This paper draws on perspectives from three different studies. One study, which focuses on youth life and lack of well-being (Sørensen et al 2011), one study on youth life on the margins of society (Katznelson et al 2015) and one study...

  1. Picture Postage

    Science.gov (United States)

    Osterer, Irv

    2009-01-01

    With the popularity of e-mail cutting into revenues, Canada Post is always searching for a marketing strategy that would encourage people to use the mail. "Picture Postage" is such an initiative. This popular program allows individuals to create their own stamps for family and friends. This opportunity also provides a vehicle for…

  2. Singular continuous spectrum for palindromic Schroedinger operators

    International Nuclear Information System (INIS)

    Hof, A.; Knill, O.; Simon, B.

    1995-01-01

    We give new examples of discrete Schroedinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potential x in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A sufficient condition for the existence of such an x is that there is a z element of X that contains arbitrarily long palindromes. Thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset in X. The class includes well-known substitutions like Fibonacci, Thue-Morse, Period Doubling, binary non-Pisot and ternary non-Pisot. We also show that the operator has no absolutely continuous spectrum for all x element of X if X derives from a primitive substitution. For potentials defined by circle maps, x n =l J (θ 0 +nα), we show that the operator has purely singular continuous spectrum for a generic subset in X for all irrational α and every half-open interval J. (orig.)

  3. Spectrum of the ballooning Schroedinger equation

    International Nuclear Information System (INIS)

    Dewar, R.L.

    1997-01-01

    The ballooning Schroedinger equation (BSE) is a model equation for investigating global modes that can, when approximated by a Wentzel-Kramers-Brillouin (WKB) ansatz, be described by a ballooning formalism locally to a field line. This second order differential equation with coefficients periodic in the independent variable θ k is assumed to apply even in cases where simple WKB quantization conditions break down, thus providing an alternative to semiclassical quantization. Also, it provides a test bed for developing more advanced WKB methods: e.g. the apparent discontinuity between quantization formulae for open-quotes trappedclose quotes and open-quotes passingclose quotes modes, whose ray paths have different topologies, is removed by extending the WKB method to include the phenomena of tunnelling and reflection. The BSE is applied to instabilities with shear in the real part of the local frequency, so that the dispersion relation is inherently complex. As the frequency shear is increased, it is found that trapped modes go over to passing modes, reducing the maximum growth rate by averaging over θ k

  4. Independent particle Schroedinger Fluid: moments of inertia

    International Nuclear Information System (INIS)

    Kan, K.K.; Griffin, J.J.

    1977-10-01

    This philosophy of the Single Particle Schroedinger Fluid, especially as regards the velocity fields which find such a natural role therein, is applied to the study of the moments of inertia of independent Fermion system. It is shown that three simplified systems exhibit the rigid-body rotational velocity field in the limit of large A, and that the leading deviations, both on the average and fluctuating, from this large A limit can be described analytically, and verified numerically. For a single particle in a Hill-Wheeler box the moments are studied numerically, and their large fluctuations identified with the specific energy level degeneracies of its parallelepiped shape. The full assemblage of these new and old results is addressed to the question of the necessary and sufficient condition that the moment have the rigid value. Counterexamples are utilized to reject some conditions, and the conjecture is argued that Unconstrained Shape Equilibrium might be the necessary and sufficient condition. The spheroidal square well problem is identified as a promising test case

  5. Quasi-periodic Schroedinger operators in one dimension, absolutely continuous spectra, Bloch waves, and integrable Hamiltonian systems

    International Nuclear Information System (INIS)

    Chierchia, L.

    1986-01-01

    In the first chapter, the eigenvalue problem for a periodic Schroedinger operator, Lf = (-d 2 /dx 2 + v)f = Ef, is viewed as a two-dimensional Hamiltonian system which is integrable in the sense of Arnold and Liouville. With the aid of the Floquet-BLoch theory, it is shown that such a system is conjugate to two harmonic oscillators with frequencies α and omega, being the rotation number for L and 2π/omega the period of the potential v. This picture is generalized in the second chapter, to quasi periodic Schroedinger operators, L/sub epsilon/, with highly irrational frequencies (omega 1 , ..., omega/sub d/), which are a small perturbation of periodic operators. In the last chapter, the absolutely continuous spectrum σ/sub ac/ of a general quasi-periodic Schroedinger operators is considered. The Radon-Nikodym derivatives (with respect to Lebesgue measure) of the spectral measures are computed in terms of special independent eigensolutions existing for almost ever E in σ/sub ac/. Finally, it is shown that weak Bloch waves always exist for almost ever E in σ/sub ac/ and the question of the existence of genuine Bloch waves is turned into a regularity problem for a certain nonlinear partial differential equation on a d-dimensional torus

  6. Universal Critical Power for Nonlinear Schroedinger Equations with a Symmetric Double Well Potential

    International Nuclear Information System (INIS)

    Sacchetti, Andrea

    2009-01-01

    Here we consider stationary states for nonlinear Schroedinger equations in any spatial dimension n with symmetric double well potentials. These states may bifurcate as the strength of the nonlinear term increases and we observe two different pictures depending on the value of the nonlinearity power: a supercritical pitchfork bifurcation, and a subcritical pitchfork bifurcation with two asymmetric branches occurring as the result of saddle-node bifurcations. We show that in the semiclassical limit, or for a large barrier between the two wells, the first kind of bifurcation always occurs when the nonlinearity power is less than a critical value; in contrast, when the nonlinearity power is larger than such a critical value then we always observe the second scenario. The remarkable fact is that such a critical value is a universal constant in the sense that it does not depend on the shape of the double well potential and on the dimension n.

  7. Spectral Target Detection using Schroedinger Eigenmaps

    Science.gov (United States)

    Dorado-Munoz, Leidy P.

    Applications of optical remote sensing processes include environmental monitoring, military monitoring, meteorology, mapping, surveillance, etc. Many of these tasks include the detection of specific objects or materials, usually few or small, which are surrounded by other materials that clutter the scene and hide the relevant information. This target detection process has been boosted lately by the use of hyperspectral imagery (HSI) since its high spectral dimension provides more detailed spectral information that is desirable in data exploitation. Typical spectral target detectors rely on statistical or geometric models to characterize the spectral variability of the data. However, in many cases these parametric models do not fit well HSI data that impacts the detection performance. On the other hand, non-linear transformation methods, mainly based on manifold learning algorithms, have shown a potential use in HSI transformation, dimensionality reduction and classification. In target detection, non-linear transformation algorithms are used as preprocessing techniques that transform the data to a more suitable lower dimensional space, where the statistical or geometric detectors are applied. One of these non-linear manifold methods is the Schroedinger Eigenmaps (SE) algorithm that has been introduced as a technique for semi-supervised classification. The core tool of the SE algorithm is the Schroedinger operator that includes a potential term that encodes prior information about the materials present in a scene, and enables the embedding to be steered in some convenient directions in order to cluster similar pixels together. A completely novel target detection methodology based on SE algorithm is proposed for the first time in this thesis. The proposed methodology does not just include the transformation of the data to a lower dimensional space but also includes the definition of a detector that capitalizes on the theory behind SE. The fact that target pixels and

  8. Algorithm for research of mathematical physics equations symmetries. Symmetries of the free Schroedinger equation

    International Nuclear Information System (INIS)

    Kotel'nikov, G.A.

    1994-01-01

    An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry

  9. Construction of stable explicit finite-difference schemes for Schroedinger type differential equations

    Science.gov (United States)

    Mickens, Ronald E.

    1989-01-01

    A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.

  10. Schroedinger operators with singular perturbation potentials

    International Nuclear Information System (INIS)

    Harrell, E.M. II.

    1976-01-01

    This is a perturbative analysis of the eigenvalues and eigenfunctions of Schroedinger operators of the form -Δ + A + lambda V, defined on the Hilbert space L 2 (R/sup n/). A is a potential function (a smooth, real multiplication operator), and V is a ''spikelike'' perturbation, i.e., a perturbative potential function which diverges at some finite point. Lambda is a small real or complex parameter. The emphasis is on one-dimensional problems, and in particular the typical example is the ''spiked harmonic oscillator'' Hamiltonian, -d 2 /dx 2 + x 2 + lambda x/sup -α/, where α is a positive constant. An earlier study by L. Detwiler and J. R. Klauder [Phys. Rev. D 11 (1975) 1436] indicated that the lowest-order corrections to the ground-state eigenvalue of the spiked harmonic oscillator with lambda greater than 0 were proportional to lambda ln lambda when α = 3, and to lambda/sup 1/(α-2) when α is greater than 3. These and analogous results for a large class of operators and arbitrary eigenvalues are proved. Explicit constants in a modified perturbation series with a complicated dependence on lambda are determined and exhibited. Higher-order corrections for real lambda and lowest-order corrections for complex lambda are also discussed. While the substance of the dissertation is mathematical, its main applications are to quantum physics. The immediate cause of interest in such problems was the use of their peculiar convergence properties by J. R. Klauder as models for the behavior of nonrenormalizable quantum field theories. However, the results of this study are likely to be of greater importance in chemical or nuclear physics, as positive spikelike perturbations represent repulsive core interactions for quantum mechanical particles. The modified perturbation series are a new calculation technique for this situation

  11. Generalized fractional Schroedinger equation with space-time fractional derivatives

    International Nuclear Information System (INIS)

    Wang Shaowei; Xu Mingyu

    2007-01-01

    In this paper the generalized fractional Schroedinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function. The Green function for free particle is also presented in this paper. Finally, we discuss the relationship between the cases of the generalized fractional Schroedinger equation and the ones in standard quantum

  12. Dispersive estimates for the Schroedinger and Klein-Gordon equations

    Energy Technology Data Exchange (ETDEWEB)

    Kopylova, Elena A [Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow (Russian Federation)

    2010-01-01

    This is a survey of results on the long-time asymptotic behaviour of solutions of the Schroedinger and Klein-Gordon equations in weighted energy norms. Results obtained from 1975 to 2001 in the spectral scattering theory of Agmon, Jensen-Kato, Jensen-Nenciu, and Murata are described for the Schroedinger equation, along with the author's recent results obtained jointly with A.I. Komech for the Klein-Gordon equation. The methods used develop the spectral approach as applied to relativistic equations. Bibliography: 40 titles.

  13. Numerical Clifford Analysis for the Non-stationary Schroedinger Equation

    International Nuclear Information System (INIS)

    Faustino, N.; Vieira, N.

    2007-01-01

    We construct a discrete fundamental solution for the parabolic Dirac operator which factorizes the non-stationary Schroedinger operator. With such fundamental solution we construct a discrete counterpart for the Teodorescu and Cauchy-Bitsadze operators and the Bergman projectors. We finalize this paper with convergence results regarding the operators and a concrete numerical example

  14. Studying the gradient flow coupling in the Schroedinger functional

    Energy Technology Data Exchange (ETDEWEB)

    Fritzsch, P. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Ramos, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2013-08-15

    We discuss the setup and features of a new definition of the running coupling in the Schroedinger functional scheme based on the gradient flow. Its suitability for a precise continuum limit in QCD is demonstrated on a set of N{sub f}=2 gauge field ensembles in a physical volume of L{proportional_to}0.4 fm.

  15. Chronoprojective invariance of the five-dimensional Schroedinger formalism

    International Nuclear Information System (INIS)

    Perrin, M.; Burdet, G.; Duval, C.

    1984-10-01

    Invariance properties of the five-dimensional Schroedinger formalism describing a quantum test particle in the Newton-Cartan theory of gravitation are studied. The geometry which underlies these invariance properties is presented as a reduction of the 0(5,2) conformal geometry various applications are given

  16. New method for solving three-dimensional Schroedinger equation

    International Nuclear Information System (INIS)

    Melezhik, V.S.

    1990-01-01

    The method derived recently for solving a multidimensional scattering problem is applied to a three-dimensional Schroedinger equation. As compared with direct three-dimensional calculations of finite elements and finite differences, this approach gives sufficiently accurate upper and lower approximations to the helium-atom binding energy, which demonstrates its efficiency. 15 refs.; 1 fig.; 2 tabs

  17. Consequences of the Schroedinger equation for atomic and molecular physics

    International Nuclear Information System (INIS)

    Thirring, W.E.

    1986-01-01

    The non-relativistic Schroedinger equation for a system of nuclei and electrons is considered and general properties of Hamiltonian H are treated and commented: self-adjontness of H, the spectrum of H, the discrete spectrum, the continuous spectrum, the limit of infinite nuclear mass, the limit of infinite nuclear charge. (G.Q.)

  18. Quantum osp-invariant non-linear Schroedinger equation

    International Nuclear Information System (INIS)

    Kulish, P.P.

    1985-04-01

    The generalizations of the non-linear Schroedinger equation (NS) associated with the orthosymplectic superalgebras are formulated. The simplest osp(1/2)-NS model is solved by the quantum inverse scattering method on a finite interval under periodic boundary conditions as well as on the wholeline in the case of a finite number of excitations. (author)

  19. Remarks on the Schroedinger operator with singular complex potentials

    International Nuclear Information System (INIS)

    Brezis, Haim; Kato, Tosio

    1979-01-01

    To describe this method in a simple case Section 2 begin with real valued potentials. The main results in Section 2 are essentially known. In Section 3 the case of complex potentials is exposed. Schroedinger operators with complex potentials have been studied by Nelson. This results were extended. Here more general singularities are exposed

  20. On the invariant measure for the nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Zhidkov, P.R.

    1991-01-01

    The invariant measure for the nonlinear Schroedinger equation is constructed. In fact, it is assumed that the nonlinearity in the equation is semilinear. The main aim of the paper is the explanation of the Fermi - Past - Ulam phenomenon. Poincare theorem gives the answer to this question. 17 refs

  1. Exact solutions for the cubic-quintic nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Zhu Jiamin; Ma Zhengyi

    2007-01-01

    In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions

  2. On the recovering of a coupled nonlinear Schroedinger potential

    Energy Technology Data Exchange (ETDEWEB)

    Corona, Gulmaro Corona [Area de Analisis Matematico y sus Aplicaciones, Universidad Autonoma Metropolitana, Atzcapotzalco, DF (Mexico)]. E-mail: ccg@hp9000a1.uam.mx

    2000-04-28

    We establish a priori conditions for a Gel'fand-Levitan (GL) integral using some results of the Fredholm theory. As consequence, we obtain a recovering formula for the potential of the coupled nonlinear Schroedinger equations. The remarkable fact is that the recovering formula is given in terms of the solutions of a classical GL-integral equation. (author)

  3. Exact solutions to two higher order nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Xu Liping; Zhang Jinliang

    2007-01-01

    Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)

  4. Asymptotic Value Distribution for Solutions of the Schroedinger Equation

    International Nuclear Information System (INIS)

    Breimesser, S. V.; Pearson, D. B.

    2000-01-01

    We consider the Dirichlet Schroedinger operator T=-(d 2 /d x 2 )+V, acting in L 2 (0,∞), where Vis an arbitrary locally integrable potential which gives rise to absolutely continuous spectrum. Without any other restrictive assumptions on the potential V, the description of asymptotics for solutions of the Schroedinger equation is carried out within the context of the theory of value distribution for boundary values of analytic functions. The large x asymptotic behaviour of the solution v(x,λ) of the equation Tf(x,λ)=λf(x,λ), for λ in the support of the absolutely continuous part μ a.c. of the spectral measure μ, is linked to the spectral properties of this measure which are determined by the boundary value of the Weyl-Titchmarsh m-function. Our main result (Theorem 1) shows that the value distribution for v'(N,λ)/v(N,λ) approaches the associated value distribution of the Herglotz function m N (z) in the limit N → ∞, where m N (z) is the Weyl-Titchmarsh m-function for the Schroedinger operator -(d 2 /d x 2 )+Vacting in L 2 (N,∞), with Dirichlet boundary condition at x=N. We will relate the analysis of spectral asymptotics for the absolutely continuous component of Schroedinger operators to geometrical properties of the upper half-plane, viewed as a hyperbolic space

  5. Travelling solitons in the parametrically driven nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Barashenkov, I.V.; Zemlyanaya, E.V.; Baer, M.

    2000-01-01

    We show that the parametrically driven nonlinear Schroedinger equation has wide classes of travelling soliton solutions, some of which are stable. For small driving strengths stable nonpropagating and moving solitons co-exist while strongly forced solitons can only be stable when moving sufficiently fast

  6. Erwin Schroedinger, Philosophy and the birth of quantum mechanics

    International Nuclear Information System (INIS)

    Bitbol, M.; Darrigol, O.

    1992-01-01

    The purpose of this collection of articles is to highlight the relation between Schroedinger's less well known research and his thoughts on quantum mechanics: philosophy, statistical mechanics, general relativity, cosmology, unified field theories, etc. Some articles are devoted to contemporary extensions of his work, and in particular on current echoes of his interpretation of quantum mechanics

  7. Erwin Schroedinger: Collected papers V. 1. Contributions to statistical mechanics

    International Nuclear Information System (INIS)

    Schroedinger, E.

    1984-01-01

    38 publications reprinted in this volume show that the interest for statistical problems accompanied Schroedinger during his entire scientific career. Already in his second paper he worked on the magnetism of solid states. The classical considerations come close to the heart of diamagnetism and also to the origin of paramagnetism. In classical investigations of the specific heat Schroedinger helped through abstract theory but also by analysing a gigantic amount of experimental material. In 1926 he and F. Kohlrausch actually played the 'Urngame of Ehrenfest' as a model of the H-curve and published the results. Inclination towards experimenting, sequences of measurements and statistical evaluation of experimental data led to papers on the foundation of the theory of probability, where he tries to put the subjective probability concept on into a systematic framework. Two earlier papers on dynamics of the elastic chain remained particularly valuable. By solving the initial value problem with Bessel-functions this many-body-problem is led to an explicit discussion. These studies are likely to be the roots of another keynote in Schroedinger's thinking, namely, the irreversibility. 1945 a statistical theory of chain-reactions was published under the inconspicuous title of 'Probability Problems in Nuclear Chemistry'. In his last work Schroedinger turns off in a wrong direction: it is that energy should only be a statistical concept and should not be conserved in elementary processes, but somehow only in the mean. These short remarks only illuminate the diversity of the material in this volume, but testify Schroedinger's deep understanding in this field. (W.K.)

  8. Solution of the Schroedinger equation by a spectral method

    International Nuclear Information System (INIS)

    Feit, M.D.; Fleck, J.A. Jr.; Steiger, A.

    1982-01-01

    A new computational method for determining the eigenvalues and eigenfunctions of the Schroedinger equation is described. Conventional methods for solving this problem rely on diagonalization of a Hamiltonian matrix or iterative numerical solutions of a time independent wave equation. The new method, in contrast, is based on the spectral properties of solutions to the time-dependent Schroedinger equation. The method requires the computation of a correlation function from a numerical solution psi(r, t). Fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system. Analysis of the location of these peaks reveals the eigenvalues with high accuracy. Additional Fourier transforms of psi(r, t) with respect to time generate the eigenfunctions. The effectiveness of the method is demonstrated for a one-dimensional asymmetric double well potential and for the two-dimensional Henon--Heiles potential

  9. New method for solving three-dimensional Schroedinger equation

    International Nuclear Information System (INIS)

    Melezhik, V.S.

    1992-01-01

    A new method is developed for solving the multidimensional Schroedinger equation without the variable separation. To solve the Schroedinger equation in a multidimensional coordinate space X, a difference grid Ω i (i=1,2,...,N) for some of variables, Ω, from X={R,Ω} is introduced and the initial partial-differential equation is reduced to a system of N differential-difference equations in terms of one of the variables R. The arising multi-channel scattering (or eigenvalue) problem is solved by the algorithm based on a continuous analog of the Newton method. The approach has been successfully tested for several two-dimensional problems (scattering on a nonspherical potential well and 'dipole' scatterer, a hydrogen atom in a homogenous magnetic field) and for a three-dimensional problem of the helium-atom bound states. (author)

  10. Schroedinger operators with point interactions and short range expansions

    International Nuclear Information System (INIS)

    Albeverio, S.; Hoeegh-Krohn, R.; Oslo Univ.

    1984-01-01

    We give a survey of recent results concerning Schroedinger operators with point interactions in R 3 . In the case where the point interactions are located at a discrete set of points we discuss results about the resolvent, the spectrum, the resonances and the scattering quantities. We also discuss the approximation of point interactions by short range local potentials (short range or low energy expansions) and the one electron model of a 3-dimensional crystal. Moreover we discuss Schroedinger operators with Coulomb plus point interactions, with applications to the determination of scattering lengths and of level shifts in mesic atoms. Further applications to the multiple well problem, to multiparticle systems, to crystals with random impurities, to polymers and quantum fields are also briefly discussed. (orig.)

  11. Integrable discretization s of derivative nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Tsuchida, Takayuki

    2002-01-01

    We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations. (author)

  12. The Schroedinger equation as a singular perturbation problem

    International Nuclear Information System (INIS)

    Jager, E.M. de; Kuepper, T.

    1978-01-01

    Comparisons are made of the eigenvalues and the corresponding eigenfunctions of the eigenvalue problem connected with the one dimensional Schroedinger equation in Hilbert space. The difference of the eigenvalues is estimated by applying Weyl's monotonicity principle and the minimum maximum principle. The difference of the eigenfunctions is estimated in L 2 norm and in maximum norm obtained by using simple tools from operator theory in Hilbert spaces. An application concerning perturbations of the Planck ideal linear oscillator is given. (author)

  13. Strong phase correlations of solitons of nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Litvak, A.G.; Mironov, V.A.; Protogenov, A.P.

    1994-06-01

    We discuss the possibility to suppress the collapse in the nonlinear 2+1 D Schroedinger equation by using the gauge theory of strong phase correlations. It is shown that invariance relative to q-deformed Hopf algebra with deformation parameter q being the fourth root of unity makes the values of the Chern-Simons term coefficient, k=2, and of the coupling constant, g=1/2, fixed; no collapsing solutions are present at those values. (author). 21 refs

  14. The quantum nonlinear Schroedinger model with point-like defect

    International Nuclear Information System (INIS)

    Caudrelier, V; Mintchev, M; Ragoucy, E

    2004-01-01

    We establish a family of point-like impurities which preserve the quantum integrability of the nonlinear Schroedinger model in 1+1 spacetime dimensions. We briefly describe the construction of the exact second quantized solution of this model in terms of an appropriate reflection-transmission algebra. The basic physical properties of the solution, including the spacetime symmetry of the bulk scattering matrix, are also discussed. (letter to the editor)

  15. Inhomogeneous critical nonlinear Schroedinger equations with a harmonic potential

    International Nuclear Information System (INIS)

    Cao Daomin; Han Pigong

    2010-01-01

    In this paper, we study the Cauchy problem of the inhomogeneous nonlinear Schroedinger equation with a harmonic potential: i∂ t u=-div(f(x)∇u)+|x| 2 u-k(x)|u| 4/N u, x is an element of R N , N≥1, which models the remarkable Bose-Einstein condensation. We discuss the existence and nonexistence results and investigate the limiting profile of blow-up solutions with critical mass.

  16. Schroedinger propagation of initial discontinuities leads to divergence of moments

    International Nuclear Information System (INIS)

    Marchewka, A.; Schuss, Z.

    2009-01-01

    We show that the large phase expansion of the Schroedinger propagation of an initially discontinuous wave function leads to the divergence of average energy, momentum, and displacement, rendering them unphysical states. If initially discontinuous wave functions are considered to be approximations to continuous ones, the determinant of the spreading rate of these averages is the maximal gradient of the initial wave function. Therefore a dilemma arises between the inclusion of discontinuous wave functions in quantum mechanics and the requirement of finite moments.

  17. Schroedinger propagation of initial discontinuities leads to divergence of moments

    Energy Technology Data Exchange (ETDEWEB)

    Marchewka, A., E-mail: avi.marchewka@gmail.co [Ruppin Academic Center, Emek-Hefer 40250 (Israel); Schuss, Z., E-mail: schuss@post.tau.ac.i [Department of Mathematics, Tel-Aviv University, Ramat-Aviv, 69978 Tel-Aviv (Israel)

    2009-09-21

    We show that the large phase expansion of the Schroedinger propagation of an initially discontinuous wave function leads to the divergence of average energy, momentum, and displacement, rendering them unphysical states. If initially discontinuous wave functions are considered to be approximations to continuous ones, the determinant of the spreading rate of these averages is the maximal gradient of the initial wave function. Therefore a dilemma arises between the inclusion of discontinuous wave functions in quantum mechanics and the requirement of finite moments.

  18. The Schroedinger's paradox and the tranformation of quantum systems

    International Nuclear Information System (INIS)

    Bitsakis, E.I.

    1980-01-01

    The Schroedinger's paradox is analysed, as an illustration of certain weaknesses of the Copenhagen's interpretation of quantum mechanics and of the limits of the quantum-mechanical description of phenomena. A realistic approach of the paradox indicates the necessity of a theory that would permit not only the calculation of probabilities, but also the description of physical processes, as taking place in space and time

  19. Iteration of some discretizations of the nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Ross, K.A.; Thompson, C.J.

    1986-01-01

    We consider several discretizations of the nonlinear Schroedinger equation which lead naturally to the study of some symmetric difference equations of the form PHIsub(n+1) + PHIsub(n-1) = f(PHIsub(n)). We find a variety of interesting and exotic behaviour from simple closed orbits to intricate patterns of orbits and loops in the (PHIsub(n+1),PHIsub(n)) phase-plane. Some analytical results for a special case are also presented. (orig.)

  20. Integrability in the theory of Schroedinger operator and harmonic analysis

    International Nuclear Information System (INIS)

    Chalykh, O.A.; Veselov, A.P.

    1993-01-01

    The algebraic integrability for the Schroedinger equation in R n and the role of the quantum Calogero-Sutherland problem and root systems in this context are discussed. For the special values of the parameters in the potential the explicit formula for the eigenfunction of the corresponding Sutherland operator is found. As an application the explicit formula for the zonal spherical functions on the symmetric spaces SU 2 * n /Sp n (type A II in Cartan notations) is presented. (orig.)

  1. Improved Rosen's conditions on bound states of Schroedinger operators

    International Nuclear Information System (INIS)

    Exner, P.

    1984-01-01

    We derive a necessary condition on a Schroedinger operator H=-Δ+V on Lsup(2)(Rsup(d)), d>=3 to have a bound state below a given energy epsilon, and a lower bound to the ground-state energy of H. These conditions are expressed in terms of the potential V alone, and generalize the recent results of Rosen to the dimensions d>3 and to the potentials that are not necessarily rapidly decreasing. Some examples are given

  2. Erwin Schroedinger and the rise of wave mechanics. I. Schroedinger's scientific work before the creation of wave mechanics

    International Nuclear Information System (INIS)

    Mehra, J.

    1987-01-01

    This paper, the first part of a three-part article, gives an account of Erwin Schroedinger's growing up and studies in Vienna, his scientific work--first in Vienna from 1911 to 1920, then in Zurich from 1920 to 1925--on the dielectric properties of matter, atmospheric electricity and radioactivity, general relativity, color theory and physiological optics, and on kinetic theory and statistical mechanics

  3. An introduction to the self-adjointness and spectral analysis of Schroedinger operators

    International Nuclear Information System (INIS)

    Simon, B.

    1977-01-01

    The author first explains the basic results about self adjointness, from a point of view which emphasizes the connection with solvability of the Schroedinger equation. He then describes four methods that define self ajoint Hamiltonians, for most Schroedinger operators and discusses types of spectra, closing by considering the essential spectrum in the two body case. (P.D.)

  4. The frictional Schroedinger-Newton equation in models of wave function collapse

    Energy Technology Data Exchange (ETDEWEB)

    Diosi, Lajos [Research Institute for Particle and Nuclear Physics, H-1525 Budapest 114, PO Box 49 (Hungary)

    2007-05-15

    Replacing the Newtonian coupling G by -iG, the Schroedinger--Newton equation becomes {sup f}rictional{sup .} Instead of the reversible Schroedinger-Newton equation, we advocate its frictional version to generate the set of pointer states for macroscopic quantum bodies.

  5. On the solution of the Schroedinger equation through continued fractions

    International Nuclear Information System (INIS)

    Mignaco, J.A.

    1979-05-01

    The domain of interest for the applications of a method to solve the Schroedinger equation through continued fractions is studied. It is argued that the method applies almost equally well to quantum mechanical regimes (lower energy levels, low energy scattering) as well as to semiclassical ones simultaneously; this is illustrated by the example of the central power law potentials r sup(ν)(ν>o). The explanation of this behaviour is given in terms of the mathematical approximations involved and its relationship to physically interesting quantities. (Author) [pt

  6. Schroedinger operators with Rudin-Shapiro potentials are not palindromic

    International Nuclear Information System (INIS)

    Allouche, J.

    1997-01-01

    We prove a conjecture of A. Hof, O. Knill and B. Simon [Commun. Math. Phys. 174, 149 endash 159 (1995)] by showing that the Rudin-Shapiro sequence is not palindromic, i.e., does not contain arbitrarily long palindromes. We prove actually this property for all paperfolding sequences and all Rudin-Shapiro sequences deduced from paperfolding sequences. As a consequence and as guessed by the above authors, their method cannot be used for establishing that discrete Schroedinger operators with Rudin-Shapiro potentials have a purely singular continuous spectrum. copyright 1997 American Institute of Physics

  7. On quantization, the generalised Schroedinger equation and classical mechanics

    International Nuclear Information System (INIS)

    Jones, K.R.W.

    1991-01-01

    A ψ-dependent linear functional operator, was defined, which solves the problem of quantization in non-relativistic quantum mechanics. Weyl ordering is implemented automatically and permits derivation of many of the quantum to classical correspondences. The parameter λ presents a natural C ∞ deformation of the dynamical structure of quantum mechanics via a non-linear integro-differential 'Generalised Schroedinger Equation', admitting an infinite family of soliton solutions. All these solutions are presented and it is shown that this equation gives an exact dynamic and energetic reproduction of classical mechanics with the correct measurement theoretic limit. 23 refs

  8. Numerical solution of the Schroedinger equation with a polynomial potential

    International Nuclear Information System (INIS)

    Campoy, G.; Palma, A.

    1986-01-01

    A numerical method for solving the Schroedinger equation for a potential expressed as a polynomial is proposed. The basic assumption relies on the asymptotic properties of the solution of this equation. It is possible to obtain the energies and the stationary state functions simultaneously. They analyze, in particular, the cases of the quartic anharmonic oscillator and a hydrogen atom perturbed by a quadratic term, obtaining its energy eigenvalues for some values of the perturbation parameter. Together with the Hellmann-Feynman theorem, they use their algorithm to calculate expectation values of x'' for arbitrary positive values of n. 4 tables

  9. Connection between Dirac and matrix Schroedinger inverse-scattering transforms

    International Nuclear Information System (INIS)

    Jaulent, M.; Leon, J.J.P.

    1978-01-01

    The connection between two applications of the inverse scattering method for solving nonlinear equations is established. The inverse method associated with the massive Dirac system (D) : (iσ 3 d/dx - i q 3 σ 1 - q 1 σ 2 + mσ 2 )Y = epsilonY is rediscovered from the inverse method associated with the 2 x 2 matrix Schroedinger equation (S) : Ysub(xx) + (k 2 -Q)Y = 0. Here Q obeys a nonlinear constraint equivalent to a linear constraint on the reflection coefficient for (S). (author)

  10. Perturbative approach to non-Markovian stochastic Schroedinger equations

    International Nuclear Information System (INIS)

    Gambetta, Jay; Wiseman, H.M.

    2002-01-01

    In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schroedinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ρ red (t) approach the exact reduced state found via Imamog-barlu ' s enlarged system method [Phys. Rev. A 50, 3650 (1994)

  11. Properties of some nonlinear Schroedinger equations motivated through information theory

    International Nuclear Information System (INIS)

    Yuan, Liew Ding; Parwani, Rajesh R

    2009-01-01

    We update our understanding of nonlinear Schroedinger equations motivated through information theory. In particular we show that a q-deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest q = 1 case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value η = 1/4 for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, η might be encoding relativistic effects.

  12. The gradient flow coupling in the Schroedinger functional

    International Nuclear Information System (INIS)

    Fritzsch, Patrick; Ramos, Alberto

    2013-01-01

    We study the perturbative behavior of the Yang-Mills gradient flow in the Schroedinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the size of the finite volume box. From our perturbative computation we estimate the size of cutoff effects of this coupling to leading order in perturbation theory. On a set of N f =2 gauge field ensembles in a physical volume of L∝0.4 fm we finally demonstrate the suitability of the coupling for a precise continuum limit due to modest cutoff effects and high statistical precision.

  13. A new method for the solution of the Schroedinger equation

    International Nuclear Information System (INIS)

    Amore, Paolo; Aranda, Alfredo; De Pace, Arturo

    2004-01-01

    We present a new method for the solution of the Schroedinger equation applicable to problems of a non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: an asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wavefunction; and, finally, a short distance scale, in which the wavefunction is sizable. The notion of optimized perturbation is then used in the last two regimes. We apply the method to the quantum anharmonic oscillator and find it suitable to treat both energy eigenvalues and wavefunctions, even for strong couplings

  14. Localization for random Schroedinger operators with correlated potentials

    Energy Technology Data Exchange (ETDEWEB)

    Von Dreifus, H [Princeton Univ., NJ (USA). Dept. of Physics; Klein, A [California Univ., Irvine (USA). Dept. of Mathematics

    1991-08-01

    We prove localization at high disorder or low energy for lattice Schroedinger operators with random potentials whose values at different lattice sites are correlated over large distances. The class of admissible random potentials for our multiscale analysis includes potentials with a stationary Gaussian distribution whose covariance function C(x,y) decays as vertical strokex-yvertical stroke{sup -{theta}}, where {theta}>0 can be arbitrarily small, and potentials whose probability distribution is a completely analytical Gibbs measure. The result for Gaussian potentials depends on a multivariable form of Nelson's best possible hypercontractive estimate. (orig.).

  15. Schroedinger invariant solutions of type IIB with enhanced supersymmetry

    Energy Technology Data Exchange (ETDEWEB)

    Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Imperial College, London (United Kingdom). Theoretical Physics Group; Imperial College, London (United Kingdom). Inst. for Mathematical Sciences

    2009-07-15

    We construct the Killing spinors for a class of supersymmetric solutions of type IIB supergravity that are invariant under the non-relativistic Schroedinger algebra. The solutions depend on a five-dimensional Sasaki- Einstein space and it has been shown that they admit two Killing spinors. Here we will show that, for generic Sasaki-Einstein space, there are special subclasses of solutions which admit six Killing spinors and we determine the corresponding superisometry algebra. We also show that for the special case that the Sasaki-Einstein space is the round five-sphere, the number of Killing spinors can be increased to twelve. (orig.)

  16. Numerical stochastic perturbation theory in the Schroedinger functional

    International Nuclear Information System (INIS)

    Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk; Dalla Brida, Mattia; Sint, Stefan; Deutsches Elektronen-Synchrotron

    2013-11-01

    The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

  17. Philosophical and methodological aspects of the Schroedinger paradox

    International Nuclear Information System (INIS)

    Juha, L.; Krajca, R.; Smatera, M.

    1989-01-01

    Methodological aspects of the foundations of quantum theory are dealt with in relation to the quantum description of macroscopic systems, biological in particular. Attention is paid to the philosophical content of the problems of 1) the logical status of the reduction postulate in quantum mechanics, and 2) the paradox of Schroedinger's cat, whose physical solution has not yet been attained. The problem of the quantum description of complex macroscopic systems is also treated, as is Herbert Froehlich's important concept of the excitation of dominant modes in biological systems. (author). 61 refs

  18. Equivalence of two alternative approaches to Schroedinger equations

    International Nuclear Information System (INIS)

    Goenuel, B; Koeksal, K

    2006-01-01

    A recently developed simple approach for the exact/approximate solution of Schroedinger equations with constant/position-dependent mass, in which the potential is considered as in the perturbation theory, is shown to be equivalent to the one leading to the construction of exactly solvable potentials via the solution of second-order differential equations in terms of known special functions. The formalism in the former solves difficulties encountered in the latter in revealing the corrections explicitly to the unperturbed piece of the solutions whereas the other obviates cumbersome procedures used in the calculations of the former

  19. Travelling solitons in the damped driven nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Barashenkov, I.V.; Zemlyanaya, E.V.

    2003-01-01

    The well known effect of the linear damping on the moving nonlinear Schroedinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable

  20. Numerical stochastic perturbation theory in the Schroedinger functional

    Energy Technology Data Exchange (ETDEWEB)

    Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2013-11-15

    The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

  1. Integrability of a system of two nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Zhukhunashvili, V.Z.

    1989-01-01

    In recent years the inverse scattering method has achieved significant successes in the integration of nonlinear models that arise in different branches of physics. However, its region of applicability is still restricted, i.e., not all nonlinear models can be integrated. In view of the great mathematical difficulties that arise in integration, it is clearly worth testing a model for integrability before turning to integration. Such a possibility is provided by the Zakharov-Schulman method. The question of the integrability of a system of two nonlinear Schroedinger equations is resolved. It is shown that the previously known cases exhaust all integrable variants

  2. Quantum gravitational corrections to the functional Schroedinger equation

    International Nuclear Information System (INIS)

    Kiefer, C.; Singh, T.P.

    1990-10-01

    We derive corrections to the Schroedinger equation which arise from the quantization of the gravitational field. This is achieved through an expansion of the full functional Wheeler-DeWitt equation with respect to powers of the Planck mass. We demonstrate that the corrections terms are independent of the factor ordering which is chosen for the gravitational kinetic term. Although the corrections are numerically extremely tiny, we show how they lead, at least in principle, to shift in the spectral lines of hydrogen type atoms. We discuss the significance of these corrections for quantum field theory near the Planck scale. (author). 35 refs

  3. Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)

    2016-07-01

    The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

  4. Chern--Simons theory in the Schroedinger representation

    International Nuclear Information System (INIS)

    Dunne, G.V.; Jackiw, R.; Trugenberger, C.A.

    1989-01-01

    We quantize the (2+1)-dimensional Chern--Simons theory in the functional Schroedinger representation. The realization of gauge transformations on states involves a 1-cocycle. We determine this cocycle; we show how solving the Gauss law constraint in the non-Abelian theory requires quantizing the parameter that normalizes the action; we trivialize the 1-cocycle with a spatially non-local cochain related to a 2-dimensional fermion determinant and we find the physical states that satisfy the Gauss law constraint. The quantum holonomy of physical states involves a contribution that is missed when the constraint is solved before quantization. We compute this quantity for the Abelian theory in Minkowski space, where it exhibits an interesting group theoretic structure. (In a note added in proof the corresponding non-Abelian computation is presented.) Also we consider coupling to external sources and offer yet another derivation of the anomalous statistics and spin of the charge and flux carrying particles---a calculation which is especially simple in the functional Schroedinger representation. copyright 1989 Academic Press, Inc

  5. Inverse Schroedinger equation and the exact wave function

    International Nuclear Information System (INIS)

    Nakatsuji, Hiroshi

    2002-01-01

    Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem

  6. On the Schroedinger representation of the Euclidean quantum field theory

    International Nuclear Information System (INIS)

    Semmler, U.

    1987-04-01

    The theme of the present thesis is the Schroedinger representation of the Euclidean quantum field theory: We define the time development of the quantum field states as functional integral in a novel, mathematically precise way. In the following we discuss the consequences which result from this approach to the Euclidean quantum field theory. Chapter 1 introduces the theory of abstract Wiener spaces which is here proved as suitable mathematical tool for the treatment of the physical problems. In chapter 2 the diffusion theory is formulated in the framework of abstract Wiener spaces. In chapter 3 we define the field functional ψ 5 u, t 7 as functional integral, determine the functional differential equation which ψ satisfies (Schroedinger equation), and summarize the consequences resulting from this. Chapter 4 is dedicated to the attempt to determine the kernel of the time-development operator, by the knowledge of which the time development of each initial state is fixed. In chapter 5 the consequences of the theory presented in chapter 3 and 4 are discussed by means of simple examples. In chapter 6 the renormalization which results for the φ 4 potential from the definition of the functional integral in chapter 3 is calculated up to the first-order perturbation theory, and it is shown that the problems in the Symanzik renormalization procedure can be removed. (orig./HSI) [de

  7. Associations From Pictures.

    Science.gov (United States)

    Pettersson, Rune

    A picture can be interpreted in different ways by various persons. There is often a difference between a picture's denotation (literal meaning), connotation (associative meaning), and private associations. Two studies were conducted in order to observe the private associations that pictures awaken in people. One study deals with associations made…

  8. Picture languages formal models for picture recognition

    CERN Document Server

    Rosenfeld, Azriel

    1979-01-01

    Computer Science and Applied Mathematics: Picture Languages: Formal Models for Picture Recognition treats pictorial pattern recognition from the formal standpoint of automata theory. This book emphasizes the capabilities and relative efficiencies of two types of automata-array automata and cellular array automata, with respect to various array recognition tasks. The array automata are simple processors that perform sequences of operations on arrays, while the cellular array automata are arrays of processors that operate on pictures in a highly parallel fashion, one processor per picture element. This compilation also reviews a collection of results on two-dimensional sequential and parallel array acceptors. Some of the analogous one-dimensional results and array grammars and their relation to acceptors are likewise covered in this text. This publication is suitable for researchers, professionals, and specialists interested in pattern recognition and automata theory.

  9. Highcrop picture tool

    OpenAIRE

    Fog, Erik

    2013-01-01

    Pictures give other impulses than words and numbers. With images, you can easily spot new opportunities. The Highcrop-tool allows for optimization of the organic arable farm based on picture-cards. The picture-cards are designed to make it easier and more inspiring to go close to the details of production. By using the picture-cards you can spot the areas, where there is a possibility to optimize the production system for better results in the future. Highcrop picture cards can be used to:...

  10. A global numerical solution of the radial Schroedinger equation by second-order perturbation theory

    International Nuclear Information System (INIS)

    Adam, G.

    1979-01-01

    A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)

  11. The Power of Pictures : Vertical Picture Angles in Power Pictures

    NARCIS (Netherlands)

    Giessner, Steffen R.; Ryan, Michelle K.; Schubert, Thomas W.; van Quaquebeke, Niels

    2011-01-01

    Conventional wisdom suggests that variations in vertical picture angle cause the subject to appear more powerful when depicted from below and less powerful when depicted from above. However, do the media actually use such associations to represent individual differences in power? We argue that the

  12. The power of pictures: Vertical picture angles in power pictures

    NARCIS (Netherlands)

    S.R. Giessner (Steffen); M.K. Ryan (Michelle); T.W. Schubert (Thomas); N. van Quaquebeke (Niels)

    2011-01-01

    textabstractAbstract: Conventional wisdom suggests that variations in vertical picture angle cause the subject to appear more powerful when depicted from below and less powerful when depicted from above. However, do the media actually use such associations to represent individual differences in

  13. Soliton-like solutions to the ordinary Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Zamboni-Rached, Michel [Universidade Estadual de Campinas (DMO/FEEC/UNICAMP), Campinas, SP (Brazil). Fac. de Engenharia Eletrica e de Computacao. Dept. de Microondas e Optica; Recami, Erasmo, E-mail: recami@mi.infn.i [Universita Statale di Bergamo, Bergamo (Italy). Facolta di Ingegneria

    2011-07-01

    In recent times it has been paid attention to the fact that (linear) wave equations admit of soliton-like solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain nite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. (author)

  14. Fractional integration, Morrey spaces and a Schroedinger equation

    International Nuclear Information System (INIS)

    Olsen, P.A.

    1995-01-01

    Let V : R 3 → R be the potential for the 3-dimensional Schroedinger operator -Δ + V. It was shown by Cwikel, Lieb and Rosenblum, [8], that the number of bound states, N(V), of -Δ + V is bounded by N(V) ≤ C ∫ R3 |V(x)| 3/2 dx. Later Fefferman and phong, [4], improved on this inequality. Make a dyadic decomposition of R 3 into cubes. Define a dyadic cube Q to be minimal with respect to ε > 0 if ∫ q |V(x)| p dx ≥ ε p |Q| 1-2p/3 and ∫ Q ' |V(x)| p dx p |Q'| 1-2p/3 for all dyadic cubes Q' contained-in Q. 10 refs., 4 figs., 1 tab

  15. Lower bounds for solutions of the Schroedinger equation

    International Nuclear Information System (INIS)

    Froese, R.G.

    1983-01-01

    For a large class of generalized N-body Hamiltonians H = -Δ + V the large absolute value x behavior of solutions to the Schroedinger equation H psi = H psi is studied. If E lies below the essential spectrum of H, then it is proved that lim R -1 log (absolute value psi/sub R/) = -α 0 R → infinity where absolute value psi/sub R/ 2 is the integral of absolute value psi 2 over a sphere of radius R and α 0 2 + E is a threshold or α 0 0. For E not necessarily below the essential spectrum of H, the same equation holds with absolute value psi/sub R/ 2 replaced by an integral of absolute value psi 2 over a spherical shell

  16. Soliton-like solutions to the ordinary Schroedinger equation

    International Nuclear Information System (INIS)

    Zamboni-Rached, Michel; Recami, Erasmo

    2011-01-01

    In recent times it has been paid attention to the fact that (linear) wave equations admit of soliton-like solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain nite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. (author)

  17. Limited-diffraction solutions to Maxwell and Schroedinger equations

    International Nuclear Information System (INIS)

    Lu, Jian-yu; Greenleaf, J.F.

    1996-10-01

    The authors have developed a new family of limited diffraction electromagnetic X-shaped waves based on the scalar X-shaped waves discovered previously. These waves are diffraction-free in theory and particle-like (wave packets), in that they maintain their shape as they propagate to an infinite distance. The 'X waves' possess (theoretically) infinitely extended 'arms' and - at least, the ones studied in this paper - have an infinite total energy: therefore, they are not physically realizable. However, they can be truncated in both space and time and 'approximated' by means of a finite aperture radiator so to get a large enough depth of interest (depth of field). In addition to the Maxwell equations, X wave solutions to the free Schroedinger equation are also obtained. Possible applications of these new waves are discussed. Finally, the authors discuss the appearance of the X-shaped solutions from the purely geometric point of view of the special relativity theory

  18. The gradient flow coupling in the Schroedinger functional

    Energy Technology Data Exchange (ETDEWEB)

    Fritzsch, Patrick [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Ramos, Alberto [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2013-01-15

    We study the perturbative behavior of the Yang-Mills gradient flow in the Schroedinger Functional, both in the continuum and on the lattice. The energy density of the flow field is used to define a running coupling at a scale given by the size of the finite volume box. From our perturbative computation we estimate the size of cutoff effects of this coupling to leading order in perturbation theory. On a set of N{sub f}=2 gauge field ensembles in a physical volume of L{proportional_to}0.4 fm we finally demonstrate the suitability of the coupling for a precise continuum limit due to modest cutoff effects and high statistical precision.

  19. Soliton interaction in the coupled mixed derivative nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Zhang Haiqiang; Tian Bo; Lue Xing; Li He; Meng Xianghua

    2009-01-01

    The bright one- and two-soliton solutions of the coupled mixed derivative nonlinear Schroedinger equations in birefringent optical fibers are obtained by using the Hirota's bilinear method. The investigation on the collision dynamics of the bright vector solitons shows that there exists complete or partial energy switching in this coupled model. Such parametric energy exchanges can be effectively controlled and quantificationally measured by analyzing the collision dynamics of the bright vector solitons. The influence of two types of nonlinear coefficient parameters on the energy of each vector soliton, is also discussed. Based on the significant energy transfer between the two components of each vector soliton, it is feasible to exploit the future applications in the design of logical gates, fiber directional couplers and quantum information processors.

  20. Extensions of the auxiliary field method to solve Schroedinger equations

    International Nuclear Information System (INIS)

    Silvestre-Brac, Bernard; Semay, Claude; Buisseret, Fabien

    2008-01-01

    It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schroedinger equation. This technique can generate the spectrum associated with an arbitrary potential V(r) starting from the analytically known spectrum of a particular potential P(r). In the present work, general important properties of the auxiliary field method are proved, such as scaling laws and independence of the results on the choice of P(r). The method is extended in order to find accurate analytical energy formulae for radial potentials of the form aP(r) + V(r), and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed

  1. Extensions of the auxiliary field method to solve Schroedinger equations

    Energy Technology Data Exchange (ETDEWEB)

    Silvestre-Brac, Bernard [LPSC Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France); Semay, Claude; Buisseret, Fabien [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)], E-mail: silvestre@lpsc.in2p3.fr, E-mail: claude.semay@umh.ac.be, E-mail: fabien.buisseret@umh.ac.be

    2008-10-24

    It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schroedinger equation. This technique can generate the spectrum associated with an arbitrary potential V(r) starting from the analytically known spectrum of a particular potential P(r). In the present work, general important properties of the auxiliary field method are proved, such as scaling laws and independence of the results on the choice of P(r). The method is extended in order to find accurate analytical energy formulae for radial potentials of the form aP(r) + V(r), and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed.

  2. Bound states for non-symmetric evolution Schroedinger potentials

    Energy Technology Data Exchange (ETDEWEB)

    Corona, Gulmaro Corona [Area de Analisis Matematico y sus Aplicaciones, Universidad Autonoma Metropolitana-Azcapotalco, Atzcapotzalco, DF (Mexico)). E-mail: ccg@correo.azc.uam.mx

    2001-09-14

    We consider the spectral problem associated with the evolution Schroedinger equation, (D{sup 2}+ k{sup 2}){phi}=u{phi}, where u is a matrix-square-valued function, with entries in the Schwartz class defined on the real line. The solution {phi}, called the wavefunction, consists of a function of one real variable, matrix-square-valued with entries in the Schwartz class. This problem has been dealt for symmetric potentials u. We found for the present case that the bound states are localized similarly to the scalar and symmetric cases, but by the zeroes of an analytic matrix-valued function. If we add an extra condition to the potential u, we can determine these states by an analytic scalar function. We do this by generalizing the scalar and symmetric cases but without using the fact that the Wronskian of a pair of wavefunction is constant. (author)

  3. Nonlinear Schroedinger equation with U(p,q) isotopical group

    International Nuclear Information System (INIS)

    Makhankov, V.G.; Pashaev, O.K.

    1981-01-01

    The properties of the nonlinear Schroedinger equation (NLS) with U(1,1) isogroup are considered in detail. This example illustrates the essential difference between the system and the well-known ''vector'' NLS, i.e. the large set of allowed boundary conditions on the fields that leads to a rich set of solutions of the system. Four types of boundary conditions and related soliton solutions are considered. The Bohr-Sommerfeld quantization allows to interpret them in terms of ''drops'' and ''bubbles'' as bound states of a large number of constituent bosons subject to the thermodynamical relations for gas mixtures. The U(1,1) system under the vanishing boundary conditions may be considered as continuous analog of the Hubbard model and therefore the paper is concluded by studying the inverse scattering equations for this case [ru

  4. Collective states of externally driven, damped nonlinear Schroedinger solitons

    International Nuclear Information System (INIS)

    Barashenkov, I.V.; Smirnov, Yu.S.

    1997-01-01

    We study bifurcations of localized stationary solitons of the externally driven, damped nonlinear Schroedinger equation iΨ t + Ψ xx + 2|Ψ| 2 Ψ=-iγΨ-h e iΩt , in the region of large γ (γ>1/2). For each pair of h and γ, there are two coexisting solitons, Ψ + and Ψ - . As the driver's strength h increases for the fixed γ, the Ψ + soliton merges with the flat background while the Ψ - forms a stationary collective state with two 'psi-pluses': Ψ - → Ψ (+ - +) . We obtain other stationary solutions and identify them as multisoliton complexes Ψ (++) , Ψ (--) , Ψ (-+) , Ψ (---) , Ψ (-+- ) etc. The corresponding intersoliton separations are compared to predictions of a variational approximation

  5. Derivation of the Schroedinger equation from stochastic mechanics

    International Nuclear Information System (INIS)

    Wallstrom, T.C.

    1988-01-01

    The thesis is divided into four largely independent chapters. The first three chapters treat mathematical problems in the theory of stochastic mechanics. The fourth chapter deals with stochastic mechanisms as a physical theory and shows that the Schroedinger equation cannot be derived from existing formulations of stochastic mechanics, as had previously been believed. Since the drift coefficients of stochastic mechanical diffusions are undefined on the nodes, or zeros of the density, an important problem has been to show that the sample paths stay away from the nodes. In Chapter 1, it is shown that for a smooth wavefunction, the closest approach to the nodes can be bounded solely in terms of the time-integrated energy. The ergodic properties of stochastic mechanical diffusions are greatly complicated by the tendency of the particles to avoid the nodes. In Chapter 2, it is shown that a sufficient condition for a stationary process to be ergodic is that there exist positive t and c such that for all x and y, p t (x,y) > cp(y), and this result is applied to show that the set of spin-1/2 diffusions is uniformly ergodic. Nelson has conjectured that in the limit as the particle's moment of inertia I goes to zero, the projections of the Bopp-Haag-Dankel diffusions onto IR 3 converge to a Markovian limit process. This conjecture is proved for the spin-1/2 case in Chapter 3, and the limit process identified as the diffusion naturally associated with the solution to the regular Pauli equation. In Chapter 4 it is shown that the general solution of the stochastic Newton equation does not correspond to a solution of the Schroedinger equation

  6. The chirally rotated Schroedinger functional. Theoretical expectations and perturbative tests

    International Nuclear Information System (INIS)

    Dalla Brida, Mattia

    2016-03-01

    The chirally rotated Schroedinger functional (χSF) with massless Wilson-type fermions provides an alternative lattice regularization of the Schroedinger functional (SF), with different lattice symmetries and a common continuum limit expected from universality. The explicit breaking of flavour and parity symmetries needs to be repaired by tuning the bare fermion mass and the coefficient of a dimension 3 boundary counterterm. Once this is achieved one expects the mechanism of automatic O(a) improvement to be operational in the χSF, in contrast to the standard formulation of the SF. This is expected to significantly improve the attainable precision for step-scaling functions of some composite operators. Furthermore, the χSF offers new strategies to determine finite renormalization constants which are traditionally obtained from chiral Ward identities. In this paper we consider a complete set of fermion bilinear operators, define corresponding correlation functions and explain the relation to their standard SF counterparts. We discuss renormalization and O(a) improvement and then use this set-up to formulate the theoretical expectations which follow from universality. Expanding the correlation functions to one-loop order of perturbation theory we then perform a number of non-trivial checks. In the process we obtain the action counterterm coefficients to one-loop order and reproduce some known perturbative results for renormalization constants of fermion bilinears. By confirming the theoretical expectations, this perturbative study lends further support to the soundness of the χSF framework and prepares the ground for non-perturbative applications.

  7. The Schroedinger functional for Gross-Neveu models

    International Nuclear Information System (INIS)

    Leder, B.

    2007-01-01

    Gross-Neveu type models with a finite number of fermion flavours are studied on a two-dimensional Euclidean space-time lattice. The models are asymptotically free and are invariant under a chiral symmetry. These similarities to QCD make them perfect benchmark systems for fermion actions used in large scale lattice QCD computations. The Schroedinger functional for the Gross-Neveu models is defined for both, Wilson and Ginsparg-Wilson fermions, and shown to be renormalisable in 1-loop lattice perturbation theory. In two dimensions four fermion interactions of the Gross-Neveu models have dimensionless coupling constants. The symmetry properties of the four fermion interaction terms and the relations among them are discussed. For Wilson fermions chiral symmetry is explicitly broken and additional terms must be included in the action. Chiral symmetry is restored up to cut-off effects by tuning the bare mass and one of the couplings. The critical mass and the symmetry restoring coupling are computed to second order in lattice perturbation theory. This result is used in the 1-loop computation of the renormalised couplings and the associated beta-functions. The renormalised couplings are defined in terms of suitable boundary-to-boundary correlation functions. In the computation the known first order coefficients of the beta-functions are reproduced. One of the couplings is found to have a vanishing betafunction. The calculation is repeated for the recently proposed Schroedinger functional with exact chiral symmetry, i.e. Ginsparg-Wilson fermions. The renormalisation pattern is found to be the same as in the Wilson case. Using the regularisation dependent finite part of the renormalised couplings, the ratio of the Lambda-parameters is computed. (orig.)

  8. A relation connecting scale transformation, Galilean transformation and Baecklund transformation for the nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Steudel, H.

    1980-01-01

    It is shown that the two-parameter manifold of Baecklund transformations known for the nonlinear Schroedinger equation can be generated from one Baecklund transformation with specified parameters by use of scale transformation and Galilean transformation. (orig.)

  9. On symmetry reduction and exact solutions of the linear one-dimensional Schroedinger equation

    International Nuclear Information System (INIS)

    Barannik, L.L.

    1996-01-01

    Symmetry reduction of the Schroedinger equation with potential is carried out on subalgebras of the Lie algebra which is the direct sum of the special Galilei algebra and one-dimensional algebra. Some new exact solutions are obtained

  10. New trace formulae for a quadratic pencil of the Schroedinger operator

    International Nuclear Information System (INIS)

    Yang Chuanfu

    2010-01-01

    This work deals with the eigenvalue problem for a quadratic pencil of the Schroedinger operator on a finite closed interval with the two-point boundary conditions. We will obtain new regularized trace formulas for this class of differential pencil.

  11. Wave-packet revival for the Schroedinger equation with position-dependent mass

    International Nuclear Information System (INIS)

    Schmidt, Alexandre G.M.

    2006-01-01

    We study the temporal evolution of solutions of 1D Schroedinger equation with position-dependent mass inside an infinite well. Revival of wave-packet is shown to exist and partial revivals are different from the usual ones

  12. Localization for off-diagonal disorder and for continuous Schroedinger operators

    International Nuclear Information System (INIS)

    Delyon, F.; Souillard, B.; Simon, B.

    1987-01-01

    We extend the proof of localization by Delyon, Levy, and Souillard to accommodate the Anderson model with off-diagonal disorder and the continuous Schroedinger equation with a random potential. (orig.)

  13. Some applications of perturbation theory to numerical integration methods for the Schroedinger equation

    International Nuclear Information System (INIS)

    Killingbeck, J.

    1979-01-01

    By using the methods of perturbation theory it is possible to construct simple formulae for the numerical integration of the Schroedinger equation, and also to calculate expectation values solely by means of simple eigenvalue calculations. (Auth.)

  14. Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng

    2004-01-01

    Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair

  15. Finiteness of the discrete spectrum of the three-particle Schroedinger operator

    International Nuclear Information System (INIS)

    Abdullaev, Janikul I.; Khalkhujaev, Axmad, M.

    2001-08-01

    We analyse the spectrum of the three-particle Schroedinger operator with pair contact and three-particle interactions on the neighboring nodes on a three-dimensional lattice. We show that the essential spectrum of this operator is the union of two segments, one of which coincides with the spectrum of an unperturbed operator and the other called two-particle branch. We will prove finiteness of the discrete spectrum of the Schroedinger operator at all parameter values of the problem. (author)

  16. Metaphor in pictures.

    Science.gov (United States)

    Kennedy, J M

    1982-01-01

    Pictures can be literal or metaphoric. Metaphoric pictures involve intended violations of standard modes of depiction that are universally recognizable. The types of metaphoric pictures correspond to major groups of verbal metaphors, with the addition of a class of pictorial runes. Often the correspondence between verbal and pictorial metaphors depends on individual features of objects and such physical parameters as change of scale. A more sophisticated analysis is required for some pictorial metaphors, involving juxtapositions of well-known objects and indirect reference.

  17. Lesson 6. Picture unsharpness

    International Nuclear Information System (INIS)

    Chikirdin, Eh.G.

    1999-01-01

    Lecture concerning the picture sharpness in biomedical radiography is presented. Notion of picture sharpness and visual acuity as an analyser of picture sharpness is specified. Attention is paid to the POX-curve as a statistical method for assessment of visual acuity. Conceptions of the sensitivity of using X-ray image visualization system together with specificity and accuracy are considered. Among indices of sharp parameters of visualization system the resolution, resolving power, picture unsharpness are discussed. It is shown that gradation and sharp characteristics of the image closely correlate that need an attention in practice to factors determining them [ru

  18. Pictures in Training

    Science.gov (United States)

    Miller, Elmo E.

    1973-01-01

    Pictures definitely seem to help training, but a study for the military finds these pictures need not be in moving form, such as films or videotape. Just how the pictorial techniques should be employed and with how much success depends on individual trainee and program differences. (KP)

  19. Analytical exact solution of the non-linear Schroedinger equation

    International Nuclear Information System (INIS)

    Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da

    2011-01-01

    Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

  20. Center manifold for nonintegrable nonlinear Schroedinger equations on the line

    International Nuclear Information System (INIS)

    Weder, R.

    2000-01-01

    In this paper we study the following nonlinear Schroedinger equation on the line, where f is real-valued, and it satisfies suitable conditions on regularity, on growth as a function of u and on decay as x → ± ∞. The generic potential, V, is real-valued and it is chosen so that the spectrum of H:= -d 2 /dx 2 +V consists of one simple negative eigenvalue and absolutely-continuous spectrum filling (0,∞). The solutions to this equation have, in general, a localized and a dispersive component. The nonlinear bound states, that bifurcate from the zero solution at the energy of the eigenvalue of H, define an invariant center manifold that consists of the orbits of time-periodic localized solutions. We prove that all small solutions approach a particular periodic orbit in the center manifold as t→ ± ∞. In general, the periodic orbits are different for t→ ± ∞. Our result implies also that the nonlinear bound states are asymptotically stable, in the sense that each solution with initial data near a nonlinear bound state is asymptotic as t→ ± ∞ to the periodic orbits of nearby nonlinear bound states that are, in general, different for t→ ± ∞. (orig.)

  1. On the chirally rotated Schroedinger functional with Wilson fermions

    International Nuclear Information System (INIS)

    Gonzalez Lopez, Jenifer

    2011-01-01

    There are many phenomena in nature, which are closely linked to the low energy regime of QCD. From a theoretical point of view, these low energy phenomena can be dealt with only by means of non-perturbative methods. It is the central goal of this thesis to provide a framework for such a nonperturbative renormalization. For that purpose, we employ a 4-dimensional lattice as a regulator of QCD. As a renormalization scheme, we propose a finite volume Schroedinger functional scheme and here in particular, the chirally rotated Schroedinger functional (χSF). We first perform analytical studies of the χSF at tree-level of perturbation theory, in the continuum and on the lattice. We study the eigenvalue spectrum of the continuum Dirac operator, equipped with chirally rotated SF boundary conditions, and derive the corresponding quark propagator. We then determine the tree-level quark propagator on the lattice, employing massless Wilson fermions as a regulator of the theory. Beyond tree-level, all studies are performed in the quenched approximation of QCD, as a first, computationally much simpler step to understand the properties of the newly proposed χSF scheme. One of the main targets of the present work, has been to perform the non-perturbative tuning of the two required coefficients of the χSF scheme, such that a well defined continuum limit can be reached. We demonstrate, as the first main result of this thesis, that the tuning is feasible and that, moreover, physical quantities are insensitive to the particular tuning condition. As in any lattice regularization with SF-like boundary conditions, there are also in the χSF a couple of counterterms at the boundaries, whose coefficients need to be tuned in order to remove the O(a) discretization effects originated at the boundaries. However, besides these boundary O(a) effects, the χSF is expected to be compatible with bulk automatic O(a)-improvement. We show here that, indeed, the scaling behavior of physical

  2. On the chirally rotated Schroedinger functional with Wilson fermions

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez Lopez, Jenifer

    2011-05-25

    There are many phenomena in nature, which are closely linked to the low energy regime of QCD. From a theoretical point of view, these low energy phenomena can be dealt with only by means of non-perturbative methods. It is the central goal of this thesis to provide a framework for such a nonperturbative renormalization. For that purpose, we employ a 4-dimensional lattice as a regulator of QCD. As a renormalization scheme, we propose a finite volume Schroedinger functional scheme and here in particular, the chirally rotated Schroedinger functional ({chi}SF). We first perform analytical studies of the {chi}SF at tree-level of perturbation theory, in the continuum and on the lattice. We study the eigenvalue spectrum of the continuum Dirac operator, equipped with chirally rotated SF boundary conditions, and derive the corresponding quark propagator. We then determine the tree-level quark propagator on the lattice, employing massless Wilson fermions as a regulator of the theory. Beyond tree-level, all studies are performed in the quenched approximation of QCD, as a first, computationally much simpler step to understand the properties of the newly proposed {chi}SF scheme. One of the main targets of the present work, has been to perform the non-perturbative tuning of the two required coefficients of the {chi}SF scheme, such that a well defined continuum limit can be reached. We demonstrate, as the first main result of this thesis, that the tuning is feasible and that, moreover, physical quantities are insensitive to the particular tuning condition. As in any lattice regularization with SF-like boundary conditions, there are also in the {chi}SF a couple of counterterms at the boundaries, whose coefficients need to be tuned in order to remove the O(a) discretization effects originated at the boundaries. However, besides these boundary O(a) effects, the {chi}SF is expected to be compatible with bulk automatic O(a)-improvement. We show here that, indeed, the scaling behavior

  3. Study of nonlinear waves described by the cubic Schroedinger equation

    International Nuclear Information System (INIS)

    Walstead, A.E.

    1980-01-01

    The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables

  4. Study of nonlinear waves described by the cubic Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Walstead, A.E.

    1980-03-12

    The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables.

  5. Investigation of solutions of boundary-value singular perturbated problem for Schroedinger equation of 4th order

    International Nuclear Information System (INIS)

    Amirkhanov, I.V.; Zhidkov, E.P.; Konnova, S.V.

    2000-01-01

    For the case of spherical-symmetrical potential we have considered the convergence of the solution of singular-perturbated Schroedinger equation of the 4th order to the solution of the corresponding standard nonrelativistic Schroedinger equation by numerical and analytical methods. The questions of existence of the solutions are explored. Numerical results are given. (author)

  6. Singular vectors and invariant equations for the Schroedinger algebra in n ≥ 3 space dimensions. The general case

    International Nuclear Information System (INIS)

    Dobrev, V. K.; Stoimenov, S.

    2010-01-01

    The singular vectors in Verma modules over the Schroedinger algebra s(n) in (n + 1)-dimensional space-time are found for the case of general representations. Using the singular vectors, hierarchies of equations invariant under Schroedinger algebras are constructed.

  7. Equivalence transformations and differential invariants of a generalized nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Senthilvelan, M; Torrisi, M; Valenti, A

    2006-01-01

    By using Lie's invariance infinitesimal criterion, we obtain the continuous equivalence transformations of a class of nonlinear Schroedinger equations with variable coefficients. We construct the differential invariants of order 1 starting from a special equivalence subalgebra E χ o . We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schr?dinger equations which can be mapped, by means of an equivalence transformation of E χ o , to the well-known cubic Schroedinger equation. We also provide the explicit form of the transformation

  8. Exponential and Bessel fitting methods for the numerical solution of the Schroedinger equation

    International Nuclear Information System (INIS)

    Raptis, A.D.; Cash, J.R.

    1987-01-01

    A new method is developed for the numerical integration of the one dimensional radial Schroedinger equation. This method involves using different integration formulae in different parts of the range of integration rather than using the same integration formula throughout. Two new integration formulae are derived, one which integrates Bessel and Neumann functions exactly and another which exactly integrates certain exponential functions. It is shown that, for large r, these new formulae are much more accurate than standard integration methods for the Schroedinger equation. The benefit of using this new approach is demonstrated by considering some numerical examples based on the Lennard-Jones potential. (orig.)

  9. Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Sun Chengfeng; Gao Hongjun

    2009-01-01

    The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.

  10. Estimate of the difference between the Kac operator and the Schroedinger semigroup

    International Nuclear Information System (INIS)

    Ichinose, T.; Satoshi, S.

    1997-01-01

    An operator norm estimate of the difference between the Kac operator and the Schroedinger semigroup is proved and used to give a variant of the Trotter product formula for Schroedinger operators in the L p operator norm. This extends Helffer's result in the L 2 operator norm to the case in the L p operator norm for more general scalar potentials and with vector potentials. The method of the proof is probabilistic based on the Feynman-Kac a nd Feynman-Kac-Ito formula. (orig.)

  11. On reduction and exact solutions of nonlinear many-dimensional Schroedinger equations

    International Nuclear Information System (INIS)

    Barannik, A.F.; Marchenko, V.A.; Fushchich, V.I.

    1991-01-01

    With the help of the canonical decomposition of an arbitrary subalgebra of the orthogonal algebra AO(n) the rank n and n-1 maximal subalgebras of the extended isochronous Galileo algebra, the rank n maximal subalgebras of the generalized extended classical Galileo algebra AG(a,n) the extended special Galileo algebra AG(2,n) and the extended whole Galileo algebra AG(3,n) are described. By using the rank n subalgebras, ansatze reducing the many dimensional Schroedinger equations to ordinary differential equations is found. With the help of the reduced equation solutions exact solutions of the Schroedinger equation are considered

  12. Non self-similar collapses described by the non-linear Schroedinger equation

    International Nuclear Information System (INIS)

    Berge, L.; Pesme, D.

    1992-01-01

    We develop a rapid method in order to find the contraction rates of the radially symmetric collapsing solutions of the nonlinear Schroedinger equation defined for space dimensions exceeding a threshold value. We explicitly determine the asymptotic behaviour of these latter solutions by solving the non stationary linear problem relative to the nonlinear Schroedinger equation. We show that the self-similar states associated with the collapsing solutions are characterized by a spatial extent which is bounded from the top by a cut-off radius

  13. Mathematical analysis of the dimensional scaling technique for the Schroedinger equation with power-law potentials

    International Nuclear Information System (INIS)

    Ding Zhonghai; Chen, Goong; Lin, Chang-Shou

    2010-01-01

    The dimensional scaling (D-scaling) technique is an innovative asymptotic expansion approach to study the multiparticle systems in molecular quantum mechanics. It enables the calculation of ground and excited state energies of quantum systems without having to solve the Schroedinger equation. In this paper, we present a mathematical analysis of the D-scaling technique for the Schroedinger equation with power-law potentials. By casting the D-scaling technique in an appropriate variational setting and studying the corresponding minimization problem, the D-scaling technique is justified rigorously. A new asymptotic dimensional expansion scheme is introduced to compute asymptotic expansions for ground state energies.

  14. Three-Step Predictor-Corrector of Exponential Fitting Method for Nonlinear Schroedinger Equations

    International Nuclear Information System (INIS)

    Tang Chen; Zhang Fang; Yan Haiqing; Luo Tao; Chen Zhanqing

    2005-01-01

    We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three-step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.

  15. The auxiliary field method and approximate analytical solutions of the Schroedinger equation with exponential potentials

    Energy Technology Data Exchange (ETDEWEB)

    Silvestre-Brac, Bernard [LPSC Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France); Semay, Claude; Buisseret, Fabien [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)], E-mail: silvestre@lpsc.in2p3.fr, E-mail: claude.semay@umh.ac.be, E-mail: fabien.buisseret@umh.ac.be

    2009-06-19

    The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies of the Schroedinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schroedinger equation with exponential potentials of the form -{alpha}r{sup {lambda}}exp(-{beta}r) can also be analytically solved by using the auxiliary field method. Closed formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn to the Yukawa potential and the pure exponential potential.

  16. The auxiliary field method and approximate analytical solutions of the Schroedinger equation with exponential potentials

    International Nuclear Information System (INIS)

    Silvestre-Brac, Bernard; Semay, Claude; Buisseret, Fabien

    2009-01-01

    The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies of the Schroedinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schroedinger equation with exponential potentials of the form -αr λ exp(-βr) can also be analytically solved by using the auxiliary field method. Closed formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn to the Yukawa potential and the pure exponential potential

  17. Quantum theory of single events: Localized de Broglie-wavelets, Schroedinger waves and classical trajectories

    International Nuclear Information System (INIS)

    Barut, A.O.

    1990-06-01

    For an arbitrary potential V with classical trajectories x-vector=g-vector(t) we construct localized oscillating three-dimensional wave lumps ψ(x-vector,t,g-vector) representing a single quantum particle. The crest of the envelope of the ripple follows the classical orbit g-vector(t) slightly modified due to potential V and ψ(x-vector,t;g-vector) satisfies the Schroedinger equation. The field energy, momentum and angular momentum calculated as integrals over all space are equal to particle energy, momentum and angular momentum. The relation to coherent states and to Schroedinger waves are also discussed. (author). 6 refs

  18. Solving the Schroedinger equation using the finite difference time domain method

    International Nuclear Information System (INIS)

    Sudiarta, I Wayan; Geldart, D J Wallace

    2007-01-01

    In this paper, we solve the Schroedinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schroedinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems

  19. On the construction of coherent states of position dependent mass Schroedinger equation endowed with effective potential

    International Nuclear Information System (INIS)

    Chithiika Ruby, V.; Senthilvelan, M.

    2010-01-01

    In this paper, we propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schroedinger equation. We use point canonical transformation method and obtain ground state eigenfunction of the position dependent mass Schroedinger equation. We fix the ladder operators in the deformed form and obtain explicit expression of the deformed superpotential in terms of mass distribution and its derivative. We also prove that these deformed operators lead to minimum uncertainty relations. Further, we illustrate our algorithm with two examples, in which the coherent states given for the second example are new.

  20. SESAME 2017 (360 pictures)

    CERN Multimedia

    Caraban Gonzalez, Noemi

    2018-01-01

    The Synchrotron-Light for Experimental Science and Applications in the Middle East (SESAME) is an independent laboratory located in Allan in the Balqa governorate of Jordan, created under the auspices of UNESCO on 30 May 2002. December 2017, Jordan Picture: Noemi Caraban

  1. Landscape as World Picture

    DEFF Research Database (Denmark)

    Wamberg, Jacob

    from Palaeolithic cave paintings through to 19th-century modernity. A structuralist comparison between this pattern and three additional fields of analysis - self-consciousness, socially-determined perception of nature, and world picture - reveals a fascinating insight into culture's macrohistorical...

  2. Intertwining relations and Darboux transformations for Schroedinger equations in (n+1) dimensions

    International Nuclear Information System (INIS)

    Schulze-Halberg, Axel

    2010-01-01

    We evaluate the intertwining relation for Schroedinger equations in (n+1) dimensions. The conditions for the existence of a Darboux transformation are analyzed and compared to their (1+1) dimensional counterparts. A complete solution of the conditions is given for (2+1) dimensions, and a Darboux transformation is constructed.

  3. On the equivalence between particular types of Navier-Stokes and non-linear Schroedinger equations

    International Nuclear Information System (INIS)

    Dietrich, K.; Vautherin, D.

    1985-01-01

    We derive a Schroedinger equation equivalent to the Navier-Stokes equation in the special case of constant kinematic viscosities. This equation contains a non-linear term similar to that proposed by Kostin for a quantum description of friction [fr

  4. Exact solutions for the quintic nonlinear Schroedinger equation with time and space modulated nonlinearities and potentials

    International Nuclear Information System (INIS)

    Belmonte-Beitia, Juan; Calvo, Gabriel F.

    2009-01-01

    In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions

  5. The exact solutions of the Schroedinger equation with the Morse potential via Laplace transforms

    International Nuclear Information System (INIS)

    Chen Gang

    2004-01-01

    In this Letter, we reduce the second-order differential equation about the one-dimensional Schroedinger equation with the Morse potential reduced to the first-order differential equation in terms of Laplace transforms and then obtain the exact bound state solutions

  6. Local and non-local Schroedinger cat states in cavity QED

    International Nuclear Information System (INIS)

    Haroche, S.

    2005-01-01

    Full text: I will review recent experiments performed on mesoscopic state superpositions of field states in cavity QED. Proposals to extend these studies to Schroedinger cat states delocalized in two cavities will be discussed. New versions of Bell's inequality tests will probe the non-local behavior of these cats and study their sensitivity to decoherence. (author)

  7. Random Schroedinger operators and the theory of disordered systems: some rigorous results

    International Nuclear Information System (INIS)

    Kunz, H.; Souillard, B.

    1981-01-01

    The authors report results on a class of finite difference Schroedinger operators with stochastic potentials. The Hamiltonian is then H(V)=-Δ+V; where Δ is the discretized Laplacian and the potential V acts as a multiplication operator. The potential V is random. (Auth.)

  8. Accurate high-lying eigenvalues of Schroedinger and Sturm-Liouville problems

    International Nuclear Information System (INIS)

    Vanden Berghe, G.; Van Daele, M.; De Meyer, H.

    1994-01-01

    A modified difference and a Numerov-like scheme have been introduced in a shooting algorithm for the determination of the (higher-lying) eigenvalues of Schroedinger equations and Sturm-Liouville problems. Some numerical experiments are introduced. Time measurements have been performed. The proposed algorithms are compared with other previously introduced shooting schemes. The structure of the eigenvalue error is discussed. ((orig.))

  9. Inverse scattering transform for the time dependent Schroedinger equation with applications to the KPI equation

    Energy Technology Data Exchange (ETDEWEB)

    Xin, Zhou [Wisconsin Univ., Madison (USA). Dept. of Mathematics

    1990-03-01

    For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.).

  10. Two simple ansaetze for obtaining exact solutions of high dispersive nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Palacios, Sergio L.

    2004-01-01

    We propose two simple ansaetze that allow us to obtain different analytical solutions of the high dispersive cubic and cubic-quintic nonlinear Schroedinger equations. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media

  11. New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation

    International Nuclear Information System (INIS)

    Yang Qin; Dai Chaoqing; Zhang Jiefang

    2005-01-01

    Some new exact travelling wave and period solutions of discrete nonlinear Schroedinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.

  12. On the spectral theory and dispersive estimates for a discrete Schroedinger equation in one dimension

    International Nuclear Information System (INIS)

    Pelinovsky, D. E.; Stefanov, A.

    2008-01-01

    Based on the recent work [Komech et al., 'Dispersive estimates for 1D discrete Schroedinger and Klein-Gordon equations', Appl. Anal. 85, 1487 (2006)] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schroedinger operator, Hφ=(-Δ+V)φ=-(φ n+1 +φ n-1 -2φ n )+V n φ n . We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates parallel e itH P a.c. (H) parallel l σ 2 →l -σ 2 -3/2 for any fixed σ>(5/2) and any t>0, where P a.c. (H) denotes the spectral projection to the absolutely continuous spectrum of H. In addition, based on the scattering theory for the discrete Jost solutions and the previous results by Stefanov and Kevrekidis [''Asymptotic behaviour of small solutions for the discrete nonlinear Schroedinger and Klein-Gordon equations,'' Nonlinearity 18, 1841 (2005)], we find new dispersive estimates parallel e itH P a.c. (H) parallel l 1 →l ∞ -1/3 , which are sharp for the discrete Schroedinger operators even for V=0

  13. Bounds on resolvents of dilated Schroedinger operators with non trapping potentials

    International Nuclear Information System (INIS)

    Duclos, P.; Klein, M.

    1985-06-01

    We provide bounds on resolvents of dilated Schroedinger operators via an exterior scaling. It is done under a non trapping condition on the potential which has a clear interpretation in classical mechanics. These bounds are a powerful tool to prove absence of resonances due to the tail of the potential in the shape resonance problem

  14. Remark on the solution of the Schroedinger equation for anharmonic oscillators via the Feynman path integral

    International Nuclear Information System (INIS)

    Rezende, J.

    1983-01-01

    We give a simple proof of Feynman's formula for the Green's function of the n-dimensional harmonic oscillator valid for every time t with Im t<=0. As a consequence the Schroedinger equation for the anharmonic oscillator is integrated and expressed by the Feynman path integral on Hilbert space. (orig.)

  15. Interrelation of alternative sets of Lax-pairs for a generalized nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Iino, Kazuhiro; Ichikawa, Yoshihiko; Wadati, Miki.

    1982-05-01

    Examination of the inverse scattering transformation schemes for a generalized nonlinear Schroedinger equation reveals the fact that the algorithm of Chen-Lee-Liu gives rise to the Lax-pairs for the squared eigenfunctions of the Wadati-Konno-Ichikawa scheme, which has been formulated as superposition of the Ablowitz-Kaup-Newell-Segur scheme and the Kaup-Newell scheme. (author)

  16. Inverse scattering transform for the time dependent Schroedinger equation with applications to the KPI equation

    International Nuclear Information System (INIS)

    Zhou Xin

    1990-01-01

    For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.)

  17. Linear and nonlinear analogues of the Schroedinger equation in the contextual approach in quantum mechanics

    International Nuclear Information System (INIS)

    Khrennikov, A.Yu.

    2005-01-01

    One derived the general evolutionary differential equation within the Hilbert space describing dynamics of the wave function. The derived contextual model is more comprehensive in contrast to a quantum one. The contextual equation may be a nonlinear one. Paper presents the conditions ensuring linearity of the evolution and derivation of the Schroedinger equation [ru

  18. Filamentary structures of the cosmic web and the nonlinear Schroedinger type equation

    International Nuclear Information System (INIS)

    Tigrak, E; Weygaert, R van de; Jones, B J T

    2011-01-01

    We show that the filamentary type structures of the cosmic web can be modeled as solitonic waves by solving the reaction diffusion system which is the hydrodynamical analogous of the nonlinear Schroedinger type equation. We find the analytical solution of this system by applying the Hirota direct method which produces the dissipative soliton solutions to formulate the dynamical evolution of the nonlinear structure formation.

  19. Continuous-time random walk as a guide to fractional Schroedinger equation

    International Nuclear Information System (INIS)

    Lenzi, E. K.; Ribeiro, H. V.; Mukai, H.; Mendes, R. S.

    2010-01-01

    We argue that the continuous-time random walk approach may be a useful guide to extend the Schroedinger equation in order to incorporate nonlocal effects, avoiding the inconsistencies raised by Jeng et al. [J. Math. Phys. 51, 062102 (2010)]. As an application, we work out a free particle in a half space, obtaining the time dependent solution by considering an arbitrary initial condition.

  20. One-dimensional Schroedinger equation as a classical dinamical problem

    International Nuclear Information System (INIS)

    Sanjines C, D.

    1990-01-01

    The analogy between the determination of the energy spectrum for periodic and localized 1 dimensional potentials and the stability for a particle under the influence of elastic forces is presented. For the particle to be confined in a bounded region of the phase space, it is necessary that the trace of the evolution matrix over a period of the periodic potential belongs to the interval (-2,2) [3]. Curiously, the same stability criterion might be applied to localized potentials and then determine the discrete spectrum for such potentials. We have found that for either periodic and localized potentials, the classical dynamical picture is more clarifying and the results are more compact. (Author)

  1. The conventional quark picture

    International Nuclear Information System (INIS)

    Dalitz, R.H.

    1976-01-01

    For baryons, mesons and deep inelastic phenomena the ideas and the problems of the conventional quark picture are pointed out. All observed baryons fit in three SU(3)-multiplets which cluster into larger SU(6)-multiplets. No mesons are known which have quantum numbers inconsistent with belonging to a SU(3) nonet or octet. The deep inelastic phenomena are described in terms of six structure functions of the proton. (BJ) [de

  2. On the quantum inverse problem for a new type of nonlinear Schroedinger equation for Alfven waves in plasma

    International Nuclear Information System (INIS)

    Sen, S.; Roy Chowdhury, A.

    1989-06-01

    The nonlinear Alfven waves are governed by the Vector Derivative nonlinear Schroedinger (VDNLS) equation, which for parallel or quasi parallel propagation reduces to the Derivative Nonlinear Schroedinger (DNLS) equation for the circularly polarized waves. We have formulated the Quantum Inverse problem for a new type of Nonlinear Schroedinger Equation which has many properties similar to the usual NLS problem but the structure of classical and quantum R matrix are distinctly different. The commutation rules of the scattering data are obtained and the Algebraic Bethe Ansatz is formulated to derive the eigenvalue equation for the energy of the excited states. 10 refs

  3. Producing colour pictures from SCAN

    International Nuclear Information System (INIS)

    Robichaud, K.

    1982-01-01

    The computer code SCAN.TSK has been written for use on the Interdata 7/32 minicomputer which will convert the pictures produced by the SCAN program into colour pictures on a colour graphics VDU. These colour pictures are a more powerful aid to detecting errors in the MONK input data than the normal lineprinter pictures. This report is intended as a user manual for using the program on the Interdata 7/32, and describes the method used to produce the pictures and gives examples of JCL, input data and of the pictures that can be produced. (U.K.)

  4. Radiodiagnosis of lung picture changes

    International Nuclear Information System (INIS)

    Kamenetskij, M.S.; Lezova, T.F.

    1988-01-01

    The roentgenological picture of changes of the lung picture in the case of different pathological states in the lungs and the heart, is described. A developed diagnostic algorithm for the syndrome of lung picture change and the rules of its application are given. 5 refs.; 9 figs

  5. Many particle systems with inverse square potential, Riccatti equation and completely integrable systems connected with Schroedinger operator

    International Nuclear Information System (INIS)

    Chudnovsky, David; Chudnovsky, G.V.

    1978-01-01

    The relations between many particle problem with inverse square potential on the line and meromorphic eigenfunctions of Schroedinger operator are presented. This gives new type of Backlund transformations for many particle problem [fr

  6. The polycentric picture

    DEFF Research Database (Denmark)

    Flensborg, Ingelise

    2008-01-01

    The polycentric picture The presentation introduces a dynamic view on children's drawings inspired by J.J.Gibson's ecological approach to visual perception. Empirical research in children's drawings will be the basis for the documentation of the fact that children's drawings contain several...... viewpoints and can be characterized as polycentric. I will talk about children's perception of environmental space and about the relations and the orientation they are establishing, which are used in the organisation of the pictorial space. The presentation serves the purpose to point out ontological...

  7. A discovery of quite exceptional importance. Schroedinger's correspondence on wave mechanics and on the cat paradoxon

    International Nuclear Information System (INIS)

    Meyenn, Karl von

    2011-01-01

    After Schroedinger has in the beginning of 1926 published his wave mechanics, he has by this opened many new physical views and perspectives, which have decidingly influenced the further development of quantum theory. Also today the Schroedinger equations forms the foundation of the whole microphysics and their far reaching applications. Therefore it is both for the scientist and for the interested layman very attractive to be informed by first hand about the more direct conditions and the problems of their origin. Letters of famous scientists and researchers have also in the past attracted the interest of the public, and many a scientist has been excited to the study by the lecture of such primary sources. The selection of about 300 letters presented here illuminates especially the origin of wave mechanics and their still controverse interpretation. An extensive introduction, comments, remarks, illustrations, and lists establish the physical and historical relations.

  8. Symbolic computation and solitons of the nonlinear Schroedinger equation in inhomogeneous optical fiber media

    International Nuclear Information System (INIS)

    Li Biao; Chen Yong

    2007-01-01

    In this paper, the inhomogeneous nonlinear Schroedinger equation with the loss/gain and the frequency chirping is investigated. With the help of symbolic computation, three families of exact analytical solutions are presented by employing the extended projective Riccati equation method. From our results, many previous known results of nonlinear Schroedinger equation obtained by some authors can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. Of optical and physical interests, soliton propagation and soliton interaction are discussed and simulated by computer, which include snake-soliton propagation and snake-solitons interaction, boomerang-like soliton propagation and boomerang-like solitons interaction, dispersion managed (DM) bright (dark) soliton propagation and DM solitons interaction

  9. Solution of Schroedinger equation for particle moving in two-well potential

    International Nuclear Information System (INIS)

    Ivanova, O.I.; Sabirov, R.Kh.

    2000-01-01

    The solution of the Schroedinger equation for the particle, moving in the two-well potential is given on the basis of a single variational method. This potential constitutes the sum of the harmonic potential and the Gaussian addition. The analytical expression for the wave function of the particle basic state is obtained. The dependence of the obtained solutions on the potential barrier height and width is studied. It is shown that the better separation of the potential barrier provides for higher accuracy of the calculations. The values of the two-well potential, whereby good agreement between the calculations and exact numerical solution of the Schroedinger equation may be expected, are presented [ru

  10. An algebraic formulation of quantum electrodynamics. [Fermi method, Schroedinger representation, Weylalgebra

    Energy Technology Data Exchange (ETDEWEB)

    Gaffney, J M

    1975-01-01

    A reappraisal of electromagnetic field theories is made and an account is given of the radiation gauge, Gupta-Bleuler and Fermi methods of quantitising the electromagnetic fields. The Weyl algebra of the vector potential is constructed and the Fermi method is then related to a certain representation of the algebra. The representation is specified by a generating functional for a state on the algebra. The Weyl algebra of the physical field is then constructed as a factor algebra. The Schroedinger representation of the algebra is then studied and it was found that the Fermi method is just a generalization of this representation to an infinite number of degrees of freedom. The Schroedinger representation of Fermi method is constructed.

  11. A q-Schroedinger algebra, its lowest weight representations and generalized q-deformed heat equations

    International Nuclear Information System (INIS)

    Dobrev, V.K.; Doebner, H.D.; Mrugalla, C.

    1995-12-01

    We give a q-deformation S-perpendicular q of the centrally extended Schroedinger algebra. We construct the lowest weight representations of S-perpendicular q , starting from the Verma modules over S-perpendicular q , finding their singular vectors and factoring the Verma submodules built on the singular vectors. We also give a vector-field realization of S-perpendicular q which provides polynomial realization of the lowest weight representations and an infinite hierarchy of q-difference equations which may be called generalized q-deformed heat equations. We also apply our methods to the on-shell q-Schroedinger algebra proposed by Floreanini and Vinet. (author). 12 refs

  12. The general Klein-Gordon-Schroedinger system: modulational instability and exact solutions

    International Nuclear Information System (INIS)

    Tang Xiaoyan; Ding Wei

    2008-01-01

    The general Klein-Gordon-Schroedinger (gKGS) system is studied where the cubic auto-interactions are introduced in both the nonlinear Schroedinger and the nonlinear Klein-Gordon fields. We first investigate the modulational instability (MI) of the system, and thus derive the general dispersion relation between the frequency and wavenumber of the modulating perturbations, which demonstrates many possibilities for the MI regions. Using the travelling wave reduction, the gKGS system is greatly simplified. Via a simple function expansion method, we obtain some exact travelling wave solutions. Under some special parameter values, some representative wave structures are graphically displayed including the kink, anti-kink, bright, dark, grey and periodic solitons

  13. Optical soliton solutions for two coupled nonlinear Schroedinger systems via Darboux transformation

    International Nuclear Information System (INIS)

    Zhang Haiqiang; Li Juan; Xu Tao; Zhang Yaxing; Hu Wei; Tian Bo

    2007-01-01

    In nonlinear optical fibers, the vector solitons can be governed by the systems of coupled nonlinear Schroedinger from polarized optical waves in an isotropic medium. Based on the Ablowitz-Kaup-Newell-Segur technology, the Darboux transformation method is successfully applied to two coupled nonlinear Schroedinger systems. With the help of symbolic computation, the bright vector one- and two-soliton solutions including one-peak and two-peak solitons are further constructed via the iterative algorithm of Darboux transformation. Through the figures for several sample solutions, the stable propagation and elastic collisions for these kinds of bright vector solitons are discussed and the possible applications are pointed out in optical communications and relevant optical experiments.In addition, the conserved quantities of such two systems, i.e., the energy, momentum and Hamiltonian, are also presented

  14. Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions

    International Nuclear Information System (INIS)

    Geng Xianguo; Su Ting

    2007-01-01

    A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived

  15. Form-preserving Transformations for the Time-dependent Schroedinger Equation in (n + 1) Dimensions

    International Nuclear Information System (INIS)

    Schulze-Halberg, Axel

    2006-01-01

    We define a form-preserving transformation (also called point canonical transformation) for the time-dependent Schroedinger equation (TDSE) in (n+1) dimensions. The form-preserving transformation is shown to be invertible and to preserve L 2 -normalizability. We give a class of time-dependent TDSEs that can be mapped onto stationary Schroedinger equations by our form-preserving transformation. As an example, we generate a solvable, time-dependent potential of Coulombic ring-shaped type together with the corresponding exact solution of the TDSE in (3+1) dimensions. We further consider TDSEs with position-dependent (effective) masses and show that there is no form-preserving transformation between them and the conventional TDSEs, if the spatial dimension of the system is higher than one

  16. Continuous analog of Newton's method for determination of quasistationary solutions of the Schroedinger equation

    International Nuclear Information System (INIS)

    Ponomarev, L.I.; Puzynin, I.V.; Puzynina, T.P.

    1975-01-01

    The paper is a part of further development of investigations in which a numerical solution method of the Schroedinger equation for the case of a discrete spectrum has been developed and applied. The suggested algorithm (CAMEN scheme) is generalized and applied to quasistationary solutions of the Schroedinger equation system. Some specific features of the CAMEN scheme realization (such as establishing boundary conditions are observed while calculating quasistationary levels of hydrogen mesic molecules. The calculations have been carried out for energies and wave functions of quasistationary states of hydrogen mesic molecules. The choice of the initial approximation, the accuracy of calculations and characteristics of the convergence of the method have been investigated. The CAMEN algorithm has been realized in the form of the FORTRAN program packet. The CAMEN scheme can be also used for solving scatering problems

  17. Quantum Gelfand-Levitan equations for nonlinear Schroedinger model of spin-1/2 particles

    International Nuclear Information System (INIS)

    Pu, F.; Zhao, B.

    1984-01-01

    The quantum Gelfand-Levitan equations for the nonlinear Schroedinger model of spin-(1/2) particles are obtained. Two Izergin-Korepin relations are used in the derivation. A new type commutation relation of L operators is introduced to get the commutation relations which are needed for the study of S matrices and Green's functions. As examples, the four-point Green's functions and the two-body S matrices are given

  18. Breather type solutions of the vector nonlinear Schroedinger equation with quasi-constant boundary conditions

    International Nuclear Information System (INIS)

    Makhan'kov, V.G.; Slavov, S.I.

    1989-01-01

    Vector nonlinear Schroedinger equations (VS3) is investigated under quasi-constant boundary conditions. New two-soliton solutions are obtained with such non-trivial dynamics that they may be called the breather solutions. A version of the basic Novikov-Dubrovin-Krichever algebro-geometrical approach is applied to obtain breather like solutions existing for all types of internal symmetry is specified are formulated in terms of the soliton velocity expressed via the parameters of the problem. 4 refs

  19. Exact solutions of fractional Schroedinger-like equation with a nonlocal term

    International Nuclear Information System (INIS)

    Jiang Xiaoyun; Xu Mingyu; Qi Haitao

    2011-01-01

    We study the time-space fractional Schroedinger equation with a nonlocal potential. By the method of Fourier transform and Laplace transform, the Green function, and hence the wave function, is expressed in terms of H-functions. Graphical analysis demonstrates that the influence of both the space-fractal parameter α and the nonlocal parameter ν on the fractional quantum system is strong. Indeed, the nonlocal potential may act similar to a fractional spatial derivative as well as fractional time derivative.

  20. SOq(N) covariant differential calculus on quantum space and quantum deformation of Schroedinger equation

    International Nuclear Information System (INIS)

    Carow-Watamura, U.; Schlieker, M.; Watamura, S.

    1991-01-01

    We construct a differential calculus on the N-dimensional non-commutative Euclidean space, i.e., the space on which the quantum group SO q (N) is acting. The differential calculus is required to be manifestly covariant under SO q (N) transformations. Using this calculus, we consider the Schroedinger equation corresponding to the harmonic oscillator in the limit of q→1. The solution of it is given by q-deformed functions. (orig.)

  1. One-dimensional Schroedinger operators with interactions singular on a discrete set

    International Nuclear Information System (INIS)

    Gesztesy, F.; Kirsch, W.

    We study the self-adjointness of Schroedinger operators -d 2 /dx 2 +V(x) on an arbitrary interval, (a,b) with V(x) locally integrable on (a,b)inverse slantX where X is a discrete set. The treatment of quantum mechanical systems describing point interactions or periodic (possibly strongly singular) potentials is thereby included and explicit examples are presented. (orig.)

  2. On a minimization of the eigenvalues of Schroedinger operator relatively domains

    International Nuclear Information System (INIS)

    Gasymov, Yu.S.; Niftiev, A.A.

    2001-01-01

    Minimization of the eigenvalues plays an important role in the operators spectral theory. The problem on the minimization of the eigenvalues of the Schroedinger operator by areas is considered in this work. The algorithm, analogous to the conditional gradient method, is proposed for the numerical solution of this problem in the common case. The result is generalized for the case of the positively determined completely continuous operator [ru

  3. On the discrete spectrum of non-self-adjoint Schroedinger differential equation with an operator coefficient

    International Nuclear Information System (INIS)

    Bayramoglu, Mehmet; Tasci, Fatih; Zeynalov, Djafar

    2004-01-01

    We study the discrete part of spectrum of a singular non-self-adjoint second-order differential equation on a semiaxis with an operator coefficient. Its boundedness is proved. The result is applied to the Schroedinger boundary value problem -Δu+q(x)u=λ 2 u, u vertical bar ∂D =0, with a complex potential q(x) in an angular domain

  4. An evaluation of diverse methods of obtaining effective Schroedinger interaction potentials for elastic scattering

    International Nuclear Information System (INIS)

    Amos, K.; Allen, L.J.; Steward, C.; Hodgson, P.E.; Sofianos, S.A.

    1995-01-01

    Direct solution of the Schroedinger equation and inversion methods of analysis of elastic scattering data are considered to evaluate the information that they can provide about the physical interaction between colliding nuclear particles. It was found that both optical model and inversion methods based upon inverse scattering theories are subject to ambiguities. Therefore, it is essential that elastic scattering data analyses are consistent with microscopic calculations of the potential. 25 refs

  5. An evaluation of diverse methods of obtaining effective Schroedinger interaction potentials for elastic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Amos, K.; Allen, L.J.; Steward, C. [Melbourne Univ., Parkville, VIC (Australia). School of Physics; Hodgson, P.E. [Oxford Univ. (United Kingdom). Dept. of Physics; Sofianos, S.A. [University of South Africa (UNISA), Pretoria (South Africa). Dept. of Physics

    1995-10-01

    Direct solution of the Schroedinger equation and inversion methods of analysis of elastic scattering data are considered to evaluate the information that they can provide about the physical interaction between colliding nuclear particles. It was found that both optical model and inversion methods based upon inverse scattering theories are subject to ambiguities. Therefore, it is essential that elastic scattering data analyses are consistent with microscopic calculations of the potential. 25 refs.

  6. Regularity of the Rotation Number for the One-Dimensional Time-Continuous Schroedinger Equation

    Energy Technology Data Exchange (ETDEWEB)

    Amor, Sana Hadj, E-mail: sana_hadjamor@yahoo.fr [Ecole Nationale d' Ingenieurs de Monastir (Tunisia)

    2012-12-15

    Starting from results already obtained for quasi-periodic co-cycles in SL(2, R), we show that the rotation number of the one-dimensional time-continuous Schroedinger equation with Diophantine frequencies and a small analytic potential has the behavior of a 1/2-Hoelder function. We give also a sub-exponential estimate of the length of the gaps which depends on its label given by the gap-labeling theorem.

  7. On exact solitary wave solutions of the nonlinear Schroedinger equation with a source

    International Nuclear Information System (INIS)

    Raju, T Solomon; Kumar, C Nagaraja; Panigrahi, Prasanta K

    2005-01-01

    We use a fractional transformation to connect the travelling wave solutions of the nonlinear Schroedinger equation (NLSE), phase locked with a source, to the elliptic equations satisfying, f-Prime ± af ± λf 3 = 0. The solutions are necessarily of rational form, containing both trigonometric and hyperbolic types as special cases. Bright and dark solitons, as well as singular solitons, are obtained in a suitable range of parameter values. (letter to the editor)

  8. Quasiseparation of variables in the Schroedinger equation with a magnetic field

    International Nuclear Information System (INIS)

    Charest, F.; Hudon, C.; Winternitz, P.

    2007-01-01

    We consider a two-dimensional integrable Hamiltonian system with a vector and scalar potential in quantum mechanics. Contrary to the case of a pure scalar potential, the existence of a second order integral of motion does not guarantee the separation of variables in the Schroedinger equation. We introduce the concept of 'quasiseparation of variables' and show that in many cases it allows us to reduce the calculation of the energy spectrum and wave functions to linear algebra

  9. Asymptotic iteration method solutions to the d-dimensional Schroedinger equation with position-dependent mass

    International Nuclear Information System (INIS)

    Yasuk, F.; Tekin, S.; Boztosun, I.

    2010-01-01

    In this study, the exact solutions of the d-dimensional Schroedinger equation with a position-dependent mass m(r)=1/(1+ζ 2 r 2 ) is presented for a free particle, V(r)=0, by using the method of point canonical transformations. The energy eigenvalues and corresponding wavefunctions for the effective potential which is to be a generalized Poeschl-Teller potential are obtained within the framework of the asymptotic iteration method.

  10. Oscillatory integrals on Hilbert spaces and Schroedinger equation with magnetic fields

    International Nuclear Information System (INIS)

    Albeverio, S.; Brzezniak, Z.

    1994-01-01

    We extend the theory of oscillatory integrals on Hilbert spaces (the mathematical version of ''Feynman path integrals'') to cover more general integrable functions, preserving the property of the integrals to have converging finite dimensional approximations. We give an application to the representation of solutions of the time dependent Schroedinger equation with a scalar and a magnetic potential by oscillatory integrals on Hilbert spaces. A relation with Ramer's functional in the corresponding probabilistic setting is found. (orig.)

  11. Nonstationary quantum mechanics. 4. Nonadiabatic properties of the Schroedinger equation in adiabatic processes

    Energy Technology Data Exchange (ETDEWEB)

    Todorov, N S [Low Temperature Department of the Institute of Solid State Physics of the Bulgarian Academy of Sciences, Sofia

    1981-04-01

    It is shown that the nonstationary Schroedinger equation does not satisfy a well-known adiabatical principle in thermodynamics. A ''renormalization procedure'' based on the possible existence of a time-irreversible basic evolution equation is proposed with the help of which one comes to agreement in a variety of specific cases of an adiabatic inclusion of a perturbing potential. The ideology of the present article rests essentially on the ideology of the preceding articles, in particular article I.

  12. Nonstationary quantum mechanics. IV. Nonadiabatic properties of the Schroedinger equation in adiabatic processes

    Energy Technology Data Exchange (ETDEWEB)

    Todorov, N S

    1981-04-01

    It is shown that the nonstationary Schroedinger equation does not satisfy a well-known adiabatical principle in thermodynamics. A ''renormalization procedure'' based on the possible existence of a time-irreversible basic evolution equation is proposed with the help of which one comes to agreement in a variety of specific cases of an adiabatic inclusion of a perturbing potential. The ideology of the present article IV rests essentially on the ideology of the preceding articles, in particular article I.

  13. The harmonic oscillator and the position dependent mass Schroedinger equation: isospectral partners and factorization operators

    International Nuclear Information System (INIS)

    Morales, J.; Ovando, G.; Pena, J. J.

    2010-01-01

    One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.

  14. The discretized Schroedinger equation and simple models for semiconductor quantum wells

    International Nuclear Information System (INIS)

    Boykin, Timothy B; Klimeck, Gerhard

    2004-01-01

    The discretized Schroedinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schroedinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schroedinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one

  15. An inverse boundary value problem for the Schroedinger operator with vector potentials in two dimensions

    International Nuclear Information System (INIS)

    Ziqi Sun

    1993-01-01

    During the past few years a considerable interest has been focused on the inverse boundary value problem for the Schroedinger operator with a scalar (electric) potential. The popularity gained by this subject seems to be due to its connection with the inverse scattering problem at fixed energy, the inverse conductivity problem and other important inverse problems. This paper deals with an inverse boundary value problem for the Schroedinger operator with vector (electric and magnetic) potentials. As in the case of the scalar potential, results of this study would have immediate consequences in the inverse scattering problem for magnetic field at fixed energy. On the other hand, inverse boundary value problems for elliptic operators are of independent interest. The study is partly devoted to the understanding of the inverse boundary value problem for a class of general elliptic operator of second order. Note that a self-adjoint elliptic operator of second order with Δ as its principal symbol can always be written as a Schroedinger operator with vector potentials

  16. Collages of granulation pictures

    International Nuclear Information System (INIS)

    Dunn, R.B.; November, L.J.

    1985-01-01

    This paper describes two small-area selection schemes that the authors have applied to CCD observations of solar granulation. The first scheme, which the authors call the ''mosaic,'' divides the 128 x 128 array into 64 subarrays each containing 16 x 16 pixels. On each picture in the burst the RMS contrast of the fine structure is measured in each subarray and compared to the corresponding value in a table that contains the highest previous RMS values. The second scheme, which the authors call a ''collage,'' is similar except the RMS value is calculated smoothly within a sliding Gaussian window over the entire scene and the value of an individual pixel is gated into the final collage whenever the RMS contrast at that pixel location exceeds that of all previous frames taken during the burst

  17. Pictures of technology

    International Nuclear Information System (INIS)

    Huber, J.

    1989-01-01

    The first part of the book describes the development of a polarised spectrum of attitudes towards science and technology over the last two decades. Positivistic attitudes that emerged from the materialistic branch of the period of Enlightenment are shown in contrast to the attitudes that stem from the philosophical line of Rousseau-romanticism-vitalism. The second part of the book presents the results of an empirical study, providing evidence for the existence of the different attitudes towards technology and the environment. The study is based on a representative opinion poll among civil servants, engineering professions, social workers, and artists. Engineers and social workers are shown to represent the two antipodes in terms of the 'dual-culture' theory. In addition, sex-specific and age-specific differences are explained, and the different pictures of technology drawn by personalities characterised by an attitude of active control in contrast to those characterised by an attitude of intuitive faith. (orig.) [de

  18. Pictures of the month

    CERN Multimedia

    Claudia Marcelloni de Oliveira

    Starting with this issue, we will publish special pictures illustrating the ongoing construction and commissioning efforts. If you wish to have a professionnal photographer immortalize your detector before it disappears in the heart of ATLAS or for a special event, don't hesitate to contact Claudia Marcelloni de Oliveira (16-3687) from the CERN photo service. Members of the pixel team preparing to insert the outermost layer (the outer of the three barrel pixel layers) into the Global Support Frame for the Pixel Detector in SR1. Ongoing work on the first Big Wheel on the C side. Exploded view of the side-C Big Wheel and the barrel cryostat. The TRT Barrel services (HV, LV, cooling liquid, active gas, flushing gas) are now completely connected and tested. Hats off to Kirill Egorov, Mike Reilly, Ben Legeyt and Godwin Mayers who managed to fit everything within the small clearance margin!

  19. Distributed picture compilation demonstration

    Science.gov (United States)

    Alexander, Richard; Anderson, John; Leal, Jeff; Mullin, David; Nicholson, David; Watson, Graham

    2004-08-01

    A physical demonstration of distributed surveillance and tracking is described. The demonstration environment is an outdoor car park overlooked by a system of four rooftop cameras. The cameras extract moving objects from the scene, and these objects are tracked in a decentralized way, over a real communication network, using the information form of the standard Kalman filter. Each node therefore has timely access to the complete global picture and because there is no single point of failure in the system, it is robust. The demonstration system and its main components are described here, with an emphasis on some of the lessons we have learned as a result of applying a corpus of distributed data fusion theory and algorithms in practice. Initial results are presented and future plans to scale up the network are also outlined.

  20. Processors and systems (picture processing)

    Energy Technology Data Exchange (ETDEWEB)

    Gemmar, P

    1983-01-01

    Automatic picture processing requires high performance computers and high transmission capacities in the processor units. The author examines the possibilities of operating processors in parallel in order to accelerate the processing of pictures. He therefore discusses a number of available processors and systems for picture processing and illustrates their capacities for special types of picture processing. He stresses the fact that the amount of storage required for picture processing is exceptionally high. The author concludes that it is as yet difficult to decide whether very large groups of simple processors or highly complex multiprocessor systems will provide the best solution. Both methods will be aided by the development of VLSI. New solutions have already been offered (systolic arrays and 3-d processing structures) but they also are subject to losses caused by inherently parallel algorithms. Greater efforts must be made to produce suitable software for multiprocessor systems. Some possibilities for future picture processing systems are discussed. 33 references.

  1. The Spectator in the Picture

    OpenAIRE

    Hopkins, Robert

    2001-01-01

    This paper considers whether pictures ever implicitly represent internal spectators of the scenes they depict, and what theoretical construal to offer of their doing so. Richard Wollheim's discussion (Painting as an Art, ch.3) is taken as the most sophisticated attempt to answer these questions. I argue that Wollheim does not provide convincing argument for his claim that some pictures implicitly represent an internal spectator with whom the viewer of the picture is to imaginatively identify....

  2. Device for transmitting pictures and device for receiving said pictures

    NARCIS (Netherlands)

    1993-01-01

    Device for transmitting television pictures in the form of transform coefficients and motion vectors. The motion vectors of a sub-picture are converted (20) into a series of difference vectors and a reference vector. Said series is subsequently applied to a variable-length encoder (22) which encodes

  3. Biophotonics: the big picture

    Science.gov (United States)

    Marcu, Laura; Boppart, Stephen A.; Hutchinson, Mark R.; Popp, Jürgen; Wilson, Brian C.

    2018-02-01

    The 5th International Conference on Biophotonics (ICOB) held April 30 to May 1, 2017, in Fremantle, Western Australia, brought together opinion leaders to discuss future directions for the field and opportunities to consider. The first session of the conference, "How to Set a Big Picture Biophotonics Agenda," was focused on setting the stage for developing a vision and strategies for translation and impact on society of biophotonic technologies. The invited speakers, panelists, and attendees engaged in discussions that focused on opportunities and promising applications for biophotonic techniques, challenges when working at the confluence of the physical and biological sciences, driving factors for advances of biophotonic technologies, and educational opportunities. We share a summary of the presentations and discussions. Three main themes from the conference are presented in this position paper that capture the current status, opportunities, challenges, and future directions of biophotonics research and key areas of applications: (1) biophotonics at the nano- to microscale level; (2) biophotonics at meso- to macroscale level; and (3) biophotonics and the clinical translation conundrum.

  4. On norm resolvent convergence of Schroedinger operators with δ'-like potentials

    International Nuclear Information System (INIS)

    Golovaty, Yu D; Hryniv, R O

    2010-01-01

    For a function V:R→R that is integrable and compactly supported, we prove the norm resolvent convergence, as ε → 0, of a family S ε of one-dimensional Schroedinger operators on the line of the form S ε :=-d 2 /dx 2 + 1/ε 2 V(x/ε). If the potential V satisfies the conditions ∫ R V(ξ)dξ=0, ∫ R ξV(ξ)dξ=-1, then the functions ε -2 V(x/ε) converge in the sense of distributions as ε → 0 to δ'(x), and the limit S 0 of S ε might be considered as a 'physically motivated' interpretation of the one-dimensional Schroedinger operator with a potential δ'. In 1985, Seba claimed that the limit operator S 0 is the direct sum of the free Schroedinger operators on positive and negative semi-axes subject to the Dirichlet condition at x = 0, which suggested that in dimension 1 there is no non-trivial Hamiltonian with the potential δ'. In this paper, we show that in fact S 0 essentially depends on V: although the above results are true generically, in the exceptional (or 'resonant') case, the limit S 0 is non-trivial and is determined by the properties of an auxiliary Sturm-Liouville spectral problem associated with V. We then set V(ξ) = αΨ(ξ) with a fixed Ψ and show that there exists a countable set of resonances {α k } ∞ k=-∞ for which a partial transmission of the wave package occurs for S 0 .

  5. Pictures in Pictures: Art History and Art Museums in Children's Picture Books

    Science.gov (United States)

    Yohlin, Elizabeth

    2012-01-01

    Children's picture books that recreate, parody, or fictionalize famous artworks and introduce the art museum experience, a genre to which I will refer as "children's art books," have become increasingly popular over the past decade. This essay explores the pedagogical implications of this trend through the family program "Picture Books and Picture…

  6. Quasi-classical derivation of the Dirac and one-particle Schroedinger equations

    International Nuclear Information System (INIS)

    Wignall, J.W.G.

    1990-08-01

    The quasi-classical approach, in which particles are regarded as extended periodic excitations of a classical nonlinear field, is for the first time applied quantitatively in the quantum domain. It is shown that the twofold intrinsic 'spin' degree of freedom possessed by an electron can be interpreted in a purely classical way, and that the Lorentz covariant incorporation of this degree of freedom requires that the spacetime evolution of an electron excitation in a prescribed external field be given by the Dirac equation and hence, in the nonrelativistic limit, by the Pauli or Schroedinger one-particle equations. 17 refs

  7. Genus two finite gap solutions to the vector nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Woodcock, Thomas; Warren, Oliver H; Elgin, John N

    2007-01-01

    A recently published article presents a technique used to derive explicit formulae for odd genus solutions to the vector nonlinear Schroedinger equation. In another article solutions of genus two are derived using a different approach which assumes a separable ansatz. In this communication, the extension of the first technique to the even genus case is discussed, and this extension is carried out explicitly for genus two. Furthermore, a birational mapping is found between the spectral curves that arise in the two approaches. (fast track communication)

  8. Chirped self-similar solutions of a generalized nonlinear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Fei Jin-Xi [Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Zheng Chun-Long [Shaoguan Univ., Guangdong (China). School of Physics and Electromechanical Engineering; Shanghai Univ. (China). Shanghai Inst. of Applied Mathematics and Mechanics

    2011-01-15

    An improved homogeneous balance principle and an F-expansion technique are used to construct exact chirped self-similar solutions to the generalized nonlinear Schroedinger equation with distributed dispersion, nonlinearity, and gain coefficients. Such solutions exist under certain conditions and impose constraints on the functions describing dispersion, nonlinearity, and distributed gain function. The results show that the chirp function is related only to the dispersion coefficient, however, it affects all of the system parameters, which influence the form of the wave amplitude. As few characteristic examples and some simple chirped self-similar waves are presented. (orig.)

  9. Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation

    International Nuclear Information System (INIS)

    Duval, C.; Kuenzle, H.P.

    1983-02-01

    The role of the Bargmann group (11-dimensional extended Galilei group) in non relativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as General Relativity and couples minimally to a complex scalar field leading to a fourdimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory

  10. Dynamical theory of neutron diffraction. [One-body Schroedinger equation, review

    Energy Technology Data Exchange (ETDEWEB)

    Sears, V F [Atomic Energy of Canada Ltd., Chalk River, Ontario. Chalk River Nuclear Labs.

    1978-10-01

    We present a review of the dynamical theory of neutron diffraction by macroscopic bodies which provides the theoretical basis for the study of neutron optics. We consider both the theory of dispersion, in which it is shown that the coherent wave in the medium satisfies a macroscopic one-body Schroedinger equation, and the theory of reflection, refraction, and diffraction in which the above equation is solved for a number of special cases of interest. The theory is illustrated with the help of experimental results obtained over the past 10 years by a number of new techniques such as neutron gravity refractometry. Pendelloesung interference, and neutron interferometry.

  11. Quantum scattering via the discretisation of Schroedinger's equation

    Energy Technology Data Exchange (ETDEWEB)

    Alexopoulos, A. [Electronic Warfare and Radar Division, Defence Science and Technology Organisation (DSTO), PO Box 1500, Edinburgh 5111 (Australia)]. E-mail: aris.alexopoulos@dsto.defence.gov.au

    2007-03-19

    We obtain the scattering matrix for particles that encounter a quantum potential by discretising Schroedinger's time independent differential equation without the need to resort to the manipulation of the eigenfunctions directly. The singularities that arise in some solutions by other methods are handled with ease including the effects of resonances while convergence is excellent in all limits with only a small number of orders required to give accurate results. Our method compares the tunnelling probability with that of the WKB theory, exact numerical solutions and the modified Airy function method.

  12. Path space measures for Dirac and Schroedinger equations: Nonstandard analytical approach

    International Nuclear Information System (INIS)

    Nakamura, T.

    1997-01-01

    A nonstandard path space *-measure is constructed to justify the path integral formula for the Dirac equation in two-dimensional space endash time. A standard measure as well as a standard path integral is obtained from it. We also show that, even for the Schroedinger equation, for which there is no standard measure appropriate for a path integral, there exists a nonstandard measure to define a *-path integral whose standard part agrees with the ordinary path integral as defined by a limit from time-slice approximant. copyright 1997 American Institute of Physics

  13. Arbitrary l-wave solutions of the Schroedinger equation for the screen Coulomb potential

    International Nuclear Information System (INIS)

    Dong, Shishan; Sun, Guohua; Dong, Shihai

    2013-01-01

    Using improved approximate schemes for centrifugal term and the singular factor 1/r appearing in potential itself, we solve the Schroedinger equation with the screen Coulomb potential for arbitrary angular momentum state l. The bound state energy levels are obtained. A closed form of normalization constant of the wave functions is also found. The numerical results show that our results are in good agreement with those obtained by other methods. The key issue is how to treat two singular points in this quantum system. (author)

  14. Solution of Schroedinger Equation for Two-Dimensional Complex Quartic Potentials

    International Nuclear Information System (INIS)

    Singh, Ram Mehar; Chand, Fakir; Mishra, S. C.

    2009-01-01

    We investigate the quasi-exact solutions of the Schroedinger wave equation for two-dimensional non-hermitian complex Hamiltonian systems within the frame work of an extended complex phase space characterized by x = x 1 + ip 3 , y = x 2 + ip 4 , p x = p 1 + ix 3 , p y = p 2 + ix 4 . Explicit expressions of the energy eigenvalues and the eigenfunctions for ground and first excited states for a complex quartic potential are obtained. Eigenvalue spectra of some variants of the complex quartic potential, including PT-symmetric one, are also worked out. (general)

  15. Transfer matrix in 1D Schroedinger problems with constant and position-dependent mass

    International Nuclear Information System (INIS)

    Perez-Alvarez, R.; Rodriguez-Coppola, H.

    1987-10-01

    We consider the transfer matrix method for obtaining properties of standard wells and barriers in one-dimensional Schroedinger problems with constant and position-dependent mass. We report the formulae for the energy levels of a well and the transmission coefficient of a barrier. We demonstrate the continuity between virtual bound states and bound states in a well of position-dependent mass and the relation between the zero energy gap states of a periodic potential problem with the corresponding energies of the non-periodic ones with transmission coefficient equal to one. The calculations were carried out for a wide class of potential profiles. (author). 30 refs, 2 figs

  16. Auxiliary fields as a tool for computing analytical solutions of the Schroedinger equation

    International Nuclear Information System (INIS)

    Silvestre-Brac, Bernard; Semay, Claude; Buisseret, Fabien

    2008-01-01

    We propose a new method to obtain approximate solutions for the Schroedinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows to find in many cases, analytical solutions. It offers a convenient way to study the qualitative features of the energy spectrum of bound states in any potential. In particular, we illustrate our method by solving the case of central potentials with power-law form and with logarithmic form. For these types of potentials, we propose very accurate analytical energy formulae which greatly improves the corresponding formulae that can be found in the literature

  17. Auxiliary fields as a tool for computing analytical solutions of the Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Silvestre-Brac, Bernard [LPSC Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France); Semay, Claude; Buisseret, Fabien [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)], E-mail: silvestre@lpsc.in2p3.fr, E-mail: claude.semay@umh.ac.be, E-mail: fabien.buisseret@umh.ac.be

    2008-07-11

    We propose a new method to obtain approximate solutions for the Schroedinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows to find in many cases, analytical solutions. It offers a convenient way to study the qualitative features of the energy spectrum of bound states in any potential. In particular, we illustrate our method by solving the case of central potentials with power-law form and with logarithmic form. For these types of potentials, we propose very accurate analytical energy formulae which greatly improves the corresponding formulae that can be found in the literature.

  18. Toward an AdS/cold atoms correspondence: A geometric realization of the Schroedinger symmetry

    International Nuclear Information System (INIS)

    Son, D. T.

    2008-01-01

    We discuss a realization of the nonrelativistic conformal group (the Schroedinger group) as the symmetry of a spacetime. We write down a toy model in which this geometry is a solution to field equations. We discuss various issues related to nonrelativistic holography. In particular, we argue that free fermions and fermions at unitarity correspond to the same bulk theory with different choices for the near-boundary asymptotics corresponding to the source and the expectation value of one operator. We describe an extended version of nonrelativistic general coordinate invariance which is realized holographically.

  19. Exact solution of the Schroedinger equation with the spin-boson Hamiltonian

    International Nuclear Information System (INIS)

    Gardas, Bartlomiej

    2011-01-01

    We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (environment). An exact solution of the Schroedinger equation with the paradigmatic spin-boson Hamiltonian is obtained. We believe that this result is a major step ahead and may ultimately contribute to the complete resolution of the problem in question. We also construct the constant of motion for the spin-boson system. In contrast to the standard techniques available within the framework of the open quantum systems theory, our analysis is based on the theory of block operator matrices.

  20. Two-dimensional differential transform method for solving linear and non-linear Schroedinger equations

    International Nuclear Information System (INIS)

    Ravi Kanth, A.S.V.; Aruna, K.

    2009-01-01

    In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.

  1. A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Non-preturbative tuning

    Energy Technology Data Exchange (ETDEWEB)

    Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik

    2012-08-23

    The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)

  2. A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Non-preturbative tuning

    International Nuclear Information System (INIS)

    Lopez, J. Gonzalez; Jansen, K.; Renner, D.B.; Shindler, A.

    2012-01-01

    The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)

  3. Chaotic properties between the nonintegrable discrete nonlinear Schroedinger equation and a nonintegrable discrete Heisenberg model

    International Nuclear Information System (INIS)

    Ding Qing

    2007-01-01

    We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model

  4. Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation

    International Nuclear Information System (INIS)

    Duval, C.; Kuenzle, H.P.

    1984-01-01

    The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as general relativity and couples minimally to a complex scalar field leading to a four-dimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory. (author)

  5. On form factors of the conjugated field in the non-linear Schroedinger model

    Energy Technology Data Exchange (ETDEWEB)

    Kozlowski, K.K.

    2011-05-15

    Izergin-Korepin's lattice discretization of the non-linear Schroedinger model along with Oota's inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator. We prove that these form factors converge, in the zero lattice spacing limit, to those of the conjugated field operator in the continuous model. We also compute the large-volume asymptotic behavior of such form factors in the continuous model. These are in particular characterized by Fredholm determinants of operators acting on closed contours. We provide a way of defining these Fredholm determinants in the case of generic paramaters. (orig.)

  6. Basic properties of the current-current correlation measure for random Schroedinger operators

    International Nuclear Information System (INIS)

    Hislop, Peter D.; Lenoble, Olivier

    2006-01-01

    The current-current correlation measure plays a crucial role in the theory of conductivity for disordered systems. We prove a Pastur-Shubin-type formula for the current-current correlation measure expressing it as a thermodynamic limit for random Schroedinger operators on the lattice and the continuum. We prove that the limit is independent of the self-adjoint boundary conditions and independent of a large family of expanding regions. We relate this finite-volume definition to the definition obtained by using the infinite-volume operators and the trace-per-unit volume

  7. Supersymmetric Solution of the Schroedinger Equation for Woods-Saxon Potential by Using the Pekeris Approximation

    International Nuclear Information System (INIS)

    Feizi, H.; Rajabi, A.A.; Shojaei, M.R.

    2011-01-01

    In this work, the three dimensional Woods-Saxon potential is studied within the context of Supersymmetry Quantum Mechanics. We have applied the SUSY method by using the Pekeris approximation to the centrifugal potential l ≠ 0 states. By application of this method, it is possible to solve the Schroedinger equation for this potential. We obtain exactly bound state spectrum and wave function of Woods-Saxon potential for nonzero angular momentum. Hamiltonian hierarchy method and the shape invariance property are used in the calculations. (authors)

  8. A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Applications

    Energy Technology Data Exchange (ETDEWEB)

    Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik

    2012-08-24

    In a previous paper (J. G. Lopez et al.,2012) we have discussed the non-perturbative tuning of the chirally rotated Schroedinger functional ({chi}SF). This tuning is required to eliminate bulk O(a) cutoff effects in physical correlation functions. Using our tuning results obtained in this paper we perform scaling and universality tests analyzing the residual O(a) cutoff effects of several step-scaling functions and we compute renormalization factors at the matching scale. As an example of possible application of the {chi}SF we compute the renormalized strange quark mass using large volume data obtained from Wilson twisted mass fermions at maximal twist. (orig.)

  9. A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Applications

    International Nuclear Information System (INIS)

    Lopez, J. Gonzalez; Jansen, K.; Renner, D.B.; Shindler, A.

    2012-01-01

    In a previous paper (J. G. Lopez et al.,2012) we have discussed the non-perturbative tuning of the chirally rotated Schroedinger functional (χSF). This tuning is required to eliminate bulk O(a) cutoff effects in physical correlation functions. Using our tuning results obtained in this paper we perform scaling and universality tests analyzing the residual O(a) cutoff effects of several step-scaling functions and we compute renormalization factors at the matching scale. As an example of possible application of the χSF we compute the renormalized strange quark mass using large volume data obtained from Wilson twisted mass fermions at maximal twist. (orig.)

  10. Solitary wave solutions as a signature of the instability in the discrete nonlinear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Arevalo, Edward, E-mail: arevalo@temf.tu-darmstadt.d [Technische Universitaet Darmstadt, Institut fuer Theorie elektromagnetischer Felder, TEMF, Schlossgartenstr. 8, D-64289 Darmstadt (Germany)

    2009-09-21

    The effect of instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schroedinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed to derive closed-form expressions for small-amplitude solitary waves. The notion that the existence of nonlinear solitary waves in discrete systems is a signature of the modulation instability is used. With the help of this notion we conjecture that instability effects on moving solitons can be qualitative estimated from the analytical solutions. Results from numerical simulations are presented to support this conjecture.

  11. From nonlinear Schroedinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

    International Nuclear Information System (INIS)

    Yang Xiao; Du Dianlou

    2010-01-01

    The Poisson structure on C N xR N is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schroedinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

  12. A Greenian approach to the solution of the Schroedinger equation for periodic lattice potentials

    International Nuclear Information System (INIS)

    Minelli, T.A.

    1976-01-01

    A modified structural Green's function (MSGF), exploiting all the information contained in the previously solved Schroedinger equation for the electron interacting with a single lattice site, has been introduced and used in order to obtain, from a Dyson-type equation, a kernel whose poles and residues give the E-vs.-k relation and, respectively, the Bloch functions. Such a formulation suggests an alternative technique for the approximate solution of the KKR equations. The MSGF formalism has been also used in order to determine the structure constants of a one-dimensional lattice in a general representation

  13. Cognitive components of picture naming.

    Science.gov (United States)

    Johnson, C J; Paivio, A; Clark, J M

    1996-07-01

    A substantial research literature documents the effects of diverse item attributes, task conditions, and participant characteristics on the case of picture naming. The authors review what the research has revealed about 3 generally accepted stages of naming a pictured object: object identification, name activation, and response generation. They also show that dual coding theory gives a coherent and plausible account of these findings without positing amodal conceptual representations, and they identify issues and methods that may further advance the understanding of picture naming and related cognitive tasks.

  14. The Picture Exchange Communication System.

    Science.gov (United States)

    Bondy, A; Frost, L

    2001-10-01

    The Picture Exchange Communication System (PECS) is an alternative/augmentative communication system that was developed to teach functional communication to children with limited speech. The approach is unique in that it teaches children to initiate communicative interactions within a social framework. This article describes the advantages to implementing PECS over traditional approaches. The PECS training protocol is described wherein children are taught to exchange a single picture for a desired item and eventually to construct picture-based sentences and use a variety of attributes in their requests. The relationship of PECS's implementation to the development of speech in previously nonvocal students is reviewed.

  15. A new hierarchy of generalized derivative nonlinear Schroedinger equations, its bi-Hamiltonian structure and finite-dimensional involutive system

    International Nuclear Information System (INIS)

    Yan, Z.; Zhang, H.

    2001-01-01

    In this paper, an isospectral problem and one associated with a new hierarchy of nonlinear evolution equations are presented. As a reduction, a representative system of new generalized derivative nonlinear Schroedinger equations in the hierarchy is given. It is shown that the hierarchy possesses bi-Hamiltonian structures by using the trace identity method and is Liouville integrable. The spectral problem is non linearized as a finite-dimensional completely integrable Hamiltonian system under a constraint between the potentials and spectral functions. Finally, the involutive solutions of the hierarchy of equations are obtained. In particular, the involutive solutions of the system of new generalized derivative nonlinear Schroedinger equations are developed

  16. Semi-classical propagation of wavepackets for the phase space Schroedinger equation: interpretation in terms of the Feichtinger algebra

    International Nuclear Information System (INIS)

    Gosson, Maurice A de

    2008-01-01

    The nearby orbit method is a powerful tool for constructing semi-classical solutions of Schroedinger's equation when the initial datum is a coherent state. In this paper, we first extend this method to arbitrary squeezed states and thereafter apply our results to the Schroedinger equation in phase space. This adaptation requires the phase-space Weyl calculus developed in previous work of ours. We also study the regularity of the semi-classical solutions from the point of view of the Feichtinger algebra familiar from the theory of modulation spaces

  17. Quaternionic factorization of the Schroedinger operator and its applications to some first-order systems of mathematical physics

    International Nuclear Information System (INIS)

    Kravchenko, Viktor G; Kravchenko, Vladislav V

    2003-01-01

    We show that an ample class of physically meaningful partial differential systems of first order such as the Dirac equation with different one-component potentials, static Maxwell's system and the system describing the force-free magnetic fields are equivalent to a single quaternionic equation which in its turn reduces in general to a Schroedinger equation with quaternionic potential, and in some situations this last can be diagonalized. The rich variety of methods developed for different problems corresponding to the Schroedinger equation can be applied to the systems considered in the present work

  18. Quaternionic factorization of the Schroedinger operator and its applications to some first-order systems of mathematical physics

    Energy Technology Data Exchange (ETDEWEB)

    Kravchenko, Viktor G [Faculdade de Ciencias y Tecnologia, Universidade do Algarve, Campus de Gambelas, 8000 Faro (Portugal); Kravchenko, Vladislav V [Depto de Telecomunicaciones, SEPI ESIME Zacatenco, Instituto Politecnico Nacional, Av. IPN S/N, Edif. 1 CP 07738, DF (Mexico)

    2003-11-07

    We show that an ample class of physically meaningful partial differential systems of first order such as the Dirac equation with different one-component potentials, static Maxwell's system and the system describing the force-free magnetic fields are equivalent to a single quaternionic equation which in its turn reduces in general to a Schroedinger equation with quaternionic potential, and in some situations this last can be diagonalized. The rich variety of methods developed for different problems corresponding to the Schroedinger equation can be applied to the systems considered in the present work.

  19. Generalized hyperbolic functions to find soliton-like solutions for a system of coupled nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Yomba, Emmanuel

    2008-01-01

    With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schroedinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons

  20. Contribution to the establishment and resolution of the Schroedinger equation in a Riemannian manifold with constant curvature

    International Nuclear Information System (INIS)

    Rasolofoson, N.G.

    2014-01-01

    The properties of a physical system may vary significantly due to the presence of matter or energy. This change can be defined by the deformation of the space which is described as the variation of its curvature. In order to describe this law of physics, we have used differential geometry and studied especially a Schroedinger equation which describes a system evolving with time on a Riemannian manifold of constant curvature. Therefore, we have established and solved the Schroedinger equation using appropriate mathematics tools. As perspective, the study of string theory may be considered. [fr

  1. Pictures, images, and recollective experience.

    Science.gov (United States)

    Dewhurst, S A; Conway, M A

    1994-09-01

    Five experiments investigated the influence of picture processing on recollective experience in recognition memory. Subjects studied items that differed in visual or imaginal detail, such as pictures versus words and high-imageability versus low-imageability words, and performed orienting tasks that directed processing either toward a stimulus as a word or toward a stimulus as a picture or image. Standard effects of imageability (e.g., the picture superiority effect and memory advantages following imagery) were obtained only in recognition judgments that featured recollective experience and were eliminated or reversed when recognition was not accompanied by recollective experience. It is proposed that conscious recollective experience in recognition memory is cued by attributes of retrieved memories such as sensory-perceptual attributes and records of cognitive operations performed at encoding.

  2. A stochastic picture of spin

    International Nuclear Information System (INIS)

    Faris, W.G.

    1981-01-01

    Dankel has shown how to incorporate spin into stochastic mechanics. The resulting non-local hidden variable theory gives an appealing picture of spin correlation experiments in which Bell's inequality is violated. (orig.)

  3. Automated lattice perturbation theory in the Schroedinger functional. Implementation and applications in HQET

    International Nuclear Information System (INIS)

    Hesse, Dirk

    2012-01-01

    The author developed the pastor software package for automated lattice perturbation theory calculations in the Schroedinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schroedinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.

  4. Finite-time quantum-to-classical transition for a Schroedinger-cat state

    International Nuclear Information System (INIS)

    Paavola, Janika; Hall, Michael J. W.; Paris, Matteo G. A.; Maniscalco, Sabrina

    2011-01-01

    The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schroedinger-cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum-to-classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well-defined physical meaning and allow a deeper understanding of the quantum-to-classical transition. Our analysis shows that, for most nonclassicality measures, the Schroedinger-cat state becomes classical after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is a prerequisite for entanglement generation our results also bridge the gap between decoherence, which is lost only asymptotically, and entanglement, which may show a ''sudden death''. In fact, whereas the loss of coherences still remains asymptotic, we emphasize that the transition from quantum to classical can indeed occur at a finite time.

  5. Automated lattice perturbation theory in the Schroedinger functional. Implementation and applications in HQET

    Energy Technology Data Exchange (ETDEWEB)

    Hesse, Dirk

    2012-07-13

    The author developed the pastor software package for automated lattice perturbation theory calculations in the Schroedinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schroedinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.

  6. Self-Similar Solutions of Variable-Coefficient Cubic-Quintic Nonlinear Schroedinger Equation with an External Potential

    International Nuclear Information System (INIS)

    Wu Hongyu; Fei Jinxi; Zheng Chunlong

    2010-01-01

    An improved homogeneous balance principle and an F-expansion technique are used to construct exact self-similar solutions to the cubic-quintic nonlinear Schroedinger equation. Such solutions exist under certain conditions, and impose constraints on the functions describing dispersion, nonlinearity, and the external potential. Some simple self-similar waves are presented. (general)

  7. Time-dependent Schroedinger equations with effective mass in (2 + 1) dimensions: intertwining relations and Darboux operators

    International Nuclear Information System (INIS)

    Cobian, Hector; Schulze-Halberg, Axel

    2011-01-01

    We construct Darboux transformations for time-dependent Schroedinger equations with position-dependent mass in (2 + 1) dimensions. Several examples illustrate our results, which complement and generalize former findings for the constant mass case in two spatial variables (Schulze-Halberg 2010 J. Math. Phys. 51 033521).

  8. The density of states for almost periodic Schroedinger operators and the frequency module: a counter-example

    International Nuclear Information System (INIS)

    Bellissard, J.

    1981-07-01

    We exhibit an example of a one-dimensional discrete Schroedinger operator with an almost periodic potential for which the steps of the density of states do not belong to the frequency module. This example is suggested by the K-theory

  9. A perturbation expansion for the nonlinear Schroedinger equation with application to the influence of nonlinear Landau damping

    International Nuclear Information System (INIS)

    Weiland, J.; Ichikawa, Y.H.; Wilhelmsson, H.

    1977-12-01

    The Bogoliubov-Mitropolsky perturbation method has been applied to the study of a perturbation on soliton solutions to the nonlinear Schroedinger equation. The results are compared to those of Karpman and Maslov using the inverse scattering method and to those by Ott and Sudan on the KdV equation. (auth.)

  10. Studies of particles statistics in one and two dimensions, based on the quantization methods of Heisenberg, Schroedinger and Feynman

    International Nuclear Information System (INIS)

    Myrheim, J.

    1993-06-01

    The thesis deals with the application of different methods to the quantization problem for system of identical particles in one and two dimensions. The standard method is the analytic quantization method due to Schroedinger, which leads to the concept of fractional statistics in one and two dimensions. Two-dimensional particles with fractional statistics are well known by the name of anyons. Two alternative quantization methods are shown by the author, the algebraic method of Heisenberg and the Feynman path integral method. The Feynman method is closely related to the Schroedinger method, whereas the Heisenberg and Schroedinger methods may give different results. The relation between the Heisenberg and Schroedinger methods is discussed. The Heisenberg method is applied to the equations of motion of vortices in superfluid helium, which have the form of Hamiltonian equations for a one-dimensional system. The same method is also discussed more generally for systems of identical particles in one and two dimensions. An application of the Feynman method to the problem of computing the equation of state for a gas of anyons is presented. 104 refs., 4 figs

  11. The essential spectrum of Schroedinger operators with asymptotically constant magnetic fields on the Poincare upper-half plane

    International Nuclear Information System (INIS)

    Inahama, Yuzuru; Shirai, Shin-ichi

    2003-01-01

    We study the essential spectrum of the magnetic Schroedinger operators on the Poincare upper-half plane and establish a hyperbolic analog of Iwatsuka's result [J. Math. Kyoto Univ. 23(3), 475-480 (1983)] on the stability of the essential spectrum under perturbations from constant magnetic fields

  12. Schroedinger centenary

    International Nuclear Information System (INIS)

    Olive, D.

    1987-01-01

    The centenary of the birth of polymath Erwin Schrodinger was marked by a suitably multidisciplinary conference in April at London's Imperial College, reflecting the impact of the man's work on physics, chemistry, molecular biology and the history and philosophy of science

  13. Schroedinger centenary

    Energy Technology Data Exchange (ETDEWEB)

    Olive, D.

    1987-07-15

    The centenary of the birth of polymath Erwin Schrodinger was marked by a suitably multidisciplinary conference in April at London's Imperial College, reflecting the impact of the man's work on physics, chemistry, molecular biology and the history and philosophy of science.

  14. Continuity and completeness in physical theory: Schroedinger`s return to the wave interpretation of quantum mechanics in the 1950`s

    Energy Technology Data Exchange (ETDEWEB)

    D`Agostino, S. [Rome Univ. (Italy)

    1992-12-31

    In the 50s, Schroedinger proposed a new conception of a continuous theory of Quantum Mechanics, which remarkably modified his 1926 ideas on ondulatory mechanics. The lack of individuality of the atomic particles presented in the new statistics, and in Heisenberg`s Indeterminacy Relations, was by him considered as an aspect of a more general crisis in the anthology itself of classical atomism. Unlike his 1926 ideas, he proposed now to represent the wave equation in an n-dimensional space and he considered second-quantization technique as the proper mathematical tool for his new physical conception. Although he accepted that space-time discontinuities and casual gaps may appear here and there on the observational level (e.g. in the Indeterminacy Relations), he was convinced that they could be made compatible with a continuous pure theory, provided one accepted a suitable conception of the theory`s epistemiological status. For him, only a continuous theory satisfied the conditions for a complete theory. On these matters, he thought he was somehow orthodox to the ideas of Hertz and Boltzmann, which were also reflected in the teaching of Exner. (author). 69 refs.

  15. Conceptual Masking: How One Picture Captures Attention from Another Picture.

    Science.gov (United States)

    Loftus, Geoffrey R.; And Others

    1988-01-01

    Five experiments studied operations of conceptual masking--the reduction of conceptual memory performance for an initial stimulus when it is followed by a masking picture process. The subjects were 337 undergraduates at the University of Washington (Seattle). Conceptual masking is distinguished from perceptual masking. (TJH)

  16. The Picture Exchange Communication System: Digital Photographs versus Picture Symbols

    Science.gov (United States)

    Jonaitis, Carmen

    2011-01-01

    The Picture Exchange Communication System (PECS) is an augmentative and alternative system (AAC) used to improve and increase communication for children with Autism Spectrum Disorder (ASD) and other developmental disorders. Research addressing the efficacy of this system is increasing; however, there is limited information published that evaluates…

  17. Vertices in the abelized picture

    International Nuclear Information System (INIS)

    Embacher, F.

    1990-01-01

    Covariant vertices of open bosonic string theory are transformed to the abelized picture. The way the pure transverse (light-cone gauge) vertex is contained therein is exhibited explicitly. The formalism shows in a quite transparent way that all further content of a covariant vertex is of gauge type. By applying the transverse projection operator in the abelized picture, an algebraic condition whether a set of Neumann coefficients define a vertex for string theory is obtained. A speculation concerning field redefinitions in string field theory is added. (Author) 33 refs

  18. The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schroedinger equation

    International Nuclear Information System (INIS)

    Leung Shingyu; Qian Jianliang

    2010-01-01

    We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.

  19. Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schroedinger's equation with Kerr law nonlinearity

    International Nuclear Information System (INIS)

    Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong

    2011-01-01

    In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.

  20. AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Zhao Dun; Zhang Yujuan; Lou Weiwei; Luo Honggang

    2011-01-01

    By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLS systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.

  1. Stability of plane wave solutions of the two-space-dimensional nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Martin, D.U.; Yuen, H.C.; Saffman, P.G.

    1980-01-01

    The stability of plane, periodic solutions of the two-dimensional nonlinear Schroedinger equation to infinitesimal, two-dimensional perturbation has been calculated and verified numerically. For standing wave disturbances, instability is found for both odd and even modes; as the period of the unperturbed solution increases, the instability associated with the odd modes remains but that associated with the even mode disappears, which is consistent with the results of Zakharov and Rubenchik, Saffman and Yuen and Ablowitz and Segur on the stability of solitons. In addition, we have identified travelling wave instabilities for the even mode perturbations which are absent in the long-wave limit. Extrapolation to the case of an unperturbed solution with infinite period suggests that these instabilities may also be present for the soliton. In other words, the soliton is unstable to odd, standing-wave perturbations, and very likely also to even, travelling-wave perturbations. (orig.)

  2. The number of bound states for a discrete Schroedinger operator on ZN, N≥1, lattices

    International Nuclear Information System (INIS)

    Karachalios, N I

    2008-01-01

    We consider the discrete Schroedinger operator -Δ d +U in Z N , N≥1 in the case of a potential with negative part in an appropriate l σ -space (decays with an appropriate rate). We present a discrete analog of the method of Li and Yau (1983 Commun. Math. Phys. 88 309-18), proving an explicit upper estimate on the number of bound states N d (0)={j:μ j ≤0}, which is independent of the dimension of the lattice. This is a major difference with the continuous counterpart estimate, which is not valid when N = 1, 2. As a consequence, a dimension-independent smallness criterion for the existence of bound states is derived in contrast to the continuous case as well as to the discrete case of vanishing potential. A short comment is made on possible applications of the results to the study of the dynamics of some particular spatially discrete nonlinear systems

  3. Schroedinger equation from 0 (h/2π) to o(h/2πinfinity)

    International Nuclear Information System (INIS)

    Voros, A.

    1985-08-01

    The Balian and Bloch idea, that the semiclassical treatment of the Schroedinger equation can be carried out exactly to all orders, o(h/2πinfinity), has been explicitly confirmed upon the time-independent equation with a polynomial potential V(q) in one degree of freedom. The global analytic structure of certain functions, which encode the full eigenvalue distribution, has indeed been computed in great detail with the complex WKB method, yielding a structure called a resurgence algebra. In the special case V(q) = q 2 sub(M), this leads to sum rules for the eigenvalues, which have been verified numerically. Inasmuch as the leading order 0(h/2π) of the WKB expansion amounts to the stationary phase evaluation of the Feynman path integral, it is a yet unsolved challenge to reproduce our results by an exact analysis of this path integral using a generalized saddle-point treatment

  4. Antibound states for a class of one-dimensional Schroedinger Operators

    Energy Technology Data Exchange (ETDEWEB)

    Angeletti, A [Camerino Univ. (Italy). Ist. di Matematica

    1980-11-01

    Let delta(x) be the Dirac's delta, q(x) element of L/sup 1/(R) L/sup 2/(R) be a real valued function, and lambda, ..mu.. element of R; we will consider the following class of one-dimensional formal Schroedinger operators on L/sup 2/(R) H(lambda,..mu..) = - (d/sup 2//dx/sup 2/) + lambdadelta(x) + ..mu..q(x). It is known that to the formal operator H(lambda, ..mu..) may be associated a selfadjoint operator H(lambda, ..mu..) on L/sup 2/(R). If q is of finite range, for lambda < 0 and /..mu../ is small enough, we prove that H(lambda,..mu..) has an antibound state; that is the resolvent of H(lambda,..mu..) has a pole on the negative real axis on the second Riemann sheet.

  5. Stability analysis of embedded solitons in the generalized third-order nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Pelinovsky, Dmitry E.; Yang Jianke

    2005-01-01

    We study the generalized third-order nonlinear Schroedinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons

  6. Structure and properties of Hughston's stochastic extension of the Schroedinger equation

    International Nuclear Information System (INIS)

    Adler, Stephen L.; Horwitz, Lawrence P.

    2000-01-01

    Hughston has recently proposed a stochastic extension of the Schroedinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston's equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston's equation to earlier work on norm-preserving stochastic equations, and show that Hughston's equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston's, suffices to give an objective interpretation of the measurement process in quantum mechanics. (c) 2000 American Institute of Physics

  7. Discreteness of the spectrum of some operator sheaves associated with a periodic Schroedinger equation

    International Nuclear Information System (INIS)

    Dyakin, V.V.; Petrukhnovskii, S.I.

    1988-01-01

    Three-dimensional periodic Schroedinger operators with potentials that are square integrable on the unit cell (single-electron model of a crystal) are considered. A description is given of the class of rational curves that do not have more than a finite number of common points with any isoenergy surface (in particular, the Fermi surface) of an arbitrary operator of the considered form. A consequence of a theorem proved in the paper is the absence on the isoenergy surfaces of elements of planes, cones, and cylinders with straight generators, and all possible paraboloids and hyperboloids. Another interesting consequence is the following assertion: The topological dimension of an isoenergy manifold does not exceed two, which justifies the use of the word surface. The results generalize the assertion of Thomas's theorem on the absence on isoenergy surfaces of straight edges

  8. Algebraic Bethe ansatz for a quantum integrable derivative nonlinear Schroedinger model

    International Nuclear Information System (INIS)

    Basu-Mallick, B.; Bhattacharyya, Tanaya

    2002-01-01

    We find that the quantum monodromy matrix associated with a derivative nonlinear Schroedinger (DNLS) model exhibits U(2) or U(1,1) symmetry depending on the sign of the related coupling constant. By using a variant of quantum inverse scattering method which is directly applicable to field theoretical models, we derive all possible commutation relations among the operator valued elements of such monodromy matrix. Thus, we obtain the commutation relation between creation and annihilation operators of quasi-particles associated with DNLS model and find out the S-matrix for two-body scattering. We also observe that, for some special values of the coupling constant, there exists an upper bound on the number of quasi-particles which can form a soliton state for the quantum DNLS model

  9. Some simple conditions of bound states of Schroedinger operators in dimension d >= 3

    International Nuclear Information System (INIS)

    Exner, P.

    1984-01-01

    A necessary condition for existence of bound states below a given energy of a Schroedinger operator H=-Δ+V on L 2 (Rsup(d)), d>=3, together with a lower bound to the ground-state energy of H are derived using the Sobolev inequalities. It generalizes some recent results to the dimensions d>3 and to the potentials that are not necessarily rapidly decreasing. Comparison to other known necessary conditions is given. The examples of the d-dimensional hydrogen-like atom and the d-dimensional harmonic oscillator are discussed. In both of them the bound to the ground-state energy becomes remarkably tight for large values of d

  10. Generalized Euler transformation for summing strongly divergent Rayleigh-Schroedinger perturbation series: the Zeeman effect

    International Nuclear Information System (INIS)

    Silverman, J.N.

    1983-01-01

    A generalized Euler transformation (GET) is introduced which provides a powerful alternative method of accurately summing strongly divergent Rayleigh-Schroedinger (RS) perturbation series when other summability methods fail or are difficult to apply. The GET is simple to implement and, unlike a number of other summation procedures, requires no a priori knowledge of the analytic properties of the function underlying the RS series. Application of the GET to the difficult problem of the RS weak-field ground-state eigenvalue series of the hydrogen atom in a magnetic field (quadratic Zeeman effect) yields sums of good accuracy over a very wide range of field strengths up to the most intense fields of 10 14 G. The GET results are compared with those obtained by other summing methods

  11. Conservation laws derived by the Neutral-Action Method. A simple application to the Schroedinger equation

    International Nuclear Information System (INIS)

    Nordbrock, U.; Kienzler, R.

    2007-01-01

    Conservation laws are a recognized tool in physical and engineering sciences. The classical procedure to construct conservation laws is to apply Noether's Theorem. It requires the existence of a Lagrange-function for the system under consideration. Two unknown sets of functions have to be found. A broader class of such laws is obtainable, if Noether's Theorem is used together with the Bessel-Hagen extension, raising the number of sets of unknown functions to three. By using the recently developed Neutral-Action Method, the same conservation laws can be obtained by calculating only one unknown set of functions. Moreover the Neutral Action Method can also be applied in the absence of a Lagrangian, since only the governing differential equations are required for this procedure. In the paper, an application of this method to the Schroedinger equation is presented. (authors)

  12. Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

    Science.gov (United States)

    Fendzi-Donfack, Emmanuel; Nguenang, Jean Pierre; Nana, Laurent

    2018-02-01

    We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range (0<α≤1) of the derivative operator and we found the traditional solutions for the limiting case of α =1. We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.

  13. Collapse instability of solitons in the nonpolynomial Schroedinger equation with dipole-dipole interactions

    International Nuclear Information System (INIS)

    Gligoric, G; Hadzievski, Lj; Maluckov, A; Malomed, B A

    2009-01-01

    A model of the Bose-Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schroedinger equation (NPSE) with additional terms describing long-range dipole-dipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially concerning their collapse-induced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions.

  14. Gauge invariance of the Rayleigh--Schroedinger time-independent perturbation theory

    International Nuclear Information System (INIS)

    Yang, K.H.

    1977-08-01

    It is shown that the Rayleigh-Schroedinger time-independent perturbation theory is gauge invariant when the operator concerned is the particle's instantaneous energy operator H/sub B/ = (1/2m)[vector p - (e/c) vector A] 2 + eV 0 . More explicitly, it is shown that the energy perturbation corrections of each individual order of every state is gauge invariant. When the vector potential is curlless, the energy corrections of all orders are shown to vanish identically regardless of the explicit form of the vector potential. The relation between causality and gauge invariance is investigated. It is shown that gauge invariance guarantees conformity with causality and violation of gauge invariance implies violation of causality

  15. Soliton on a cnoidal wave background in the coupled nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Shin, H J

    2004-01-01

    An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schroedinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the previously known soliton solutions of dark-bright pair. Here a dark soliton resides on a cnoidal wave instead of on a constant background. It also exhibits a new type of soliton solution in a self-focusing medium, which describes a breakup of a generalized dark-bright pair into another generalized dark-bright pair and an 'oscillating' soliton. We calculate the shift of the crest of the cnoidal wave along a soliton and the moving direction of the soliton on a cnoidal wave

  16. Antibound states for a class of one-dimensional Schroedinger Operators

    International Nuclear Information System (INIS)

    Angeletti, A.

    1980-01-01

    Let delta(x) be the Dirac's delta, q(x) element of L 1 (R) L 2 (R) be a real valued function, and lambda, μ element of R; we will consider the following class of one-dimensional formal Schroedinger operators on L 2 (R) H(lambda,μ) = - (d 2 /dx 2 ) + lambdadelta(x) + μq(x). It is known that to the formal operator H(lambda, μ) may be associated a selfadjoint operator H(lambda, μ) on L 2 (R). If q is of finite range, for lambda < 0 and /μ/ is small enough, we prove that H(lambda,μ) has an antibound state; that is the resolvent of H(lambda,μ) has a pole on the negative real axis on the second Riemann sheet. (orig.)

  17. Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions

    Science.gov (United States)

    Hirschfelder, J. O.; Certain, P. R.

    1974-01-01

    A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

  18. Computation of a long-time evolution in a Schroedinger system

    International Nuclear Information System (INIS)

    Girard, R.; Kroeger, H.; Labelle, P.; Bajzer, Z.

    1988-01-01

    We compare different techniques for the computation of a long-time evolution and the S matrix in a Schroedinger system. As an application we consider a two-nucleon system interacting via the Yamaguchi potential. We suggest computation of the time evolution for a very short time using Pade approximants, the long-time evolution being obtained by iterative squaring. Within the technique of strong approximation of Moller wave operators (SAM) we compare our calculation with computation of the time evolution in the eigenrepresentation of the Hamiltonian and with the standard Lippmann-Schwinger solution for the S matrix. We find numerical agreement between these alternative methods for time-evolution computation up to half the number of digits of internal machine precision, and fairly rapid convergence of both techniques towards the Lippmann-Schwinger solution

  19. The Schroedinger-Newton equation as model of self-gravitating quantum systems

    International Nuclear Information System (INIS)

    Grossardt, Andre

    2013-01-01

    The Schroedinger-Newton equation (SN equation) describes a quantummechanical one-particle-system with gravitational self-interaction and might play a role answering the question if gravity must be quantised. As non-relativistic limit of semi-classical gravity, it provides testable predictions of the effects that classical gravity has on genuinely quantum mechanical systems in the mass regime between a few thousand proton masses and the Planck mass, which is experimentally unexplored. In this thesis I subsume the mathematical properties of the SN equation and justify it as a physical model. I will give a short outline of the controversial debate around semi-classical gravity as a fundamental theory, along with the idea of the SN equation as a model of quantum state reduction. Subsequently, I will respond to frequent objections against nonlinear Schrodinger equations. I will show how the SN equation can be obtained from Einstein's General Relativity coupled to either a KleinGordon or a Dirac equation, in the same sense as the linear Schroedinger equation can be derived in flat Minkowski space-time. The equation is, to this effect, a non-relativistic approximation of the semi-classical Einstein equations. Additionally, I will discuss, first by means of analytic estimations and later numerically, in which parameter range effects of gravitational selfinteraction - e.g. in molecular-interferometry experiments - should be expected. Besides the one-particle SN equation I will provide justification for a modified equation describing the centre-of-mass wave-function of a many-particle system. Furthermore, for this modified equation, I will examine, numerically, the consequences for experiments. Although one arrives at the conclusion that no effects of the SN equation can be expected for masses up to six or seven orders of magnitude above those considered in contemporary molecular interferometry experiments, tests of the equation, for example in satellite experiments, seem

  20. Every Picture Tells a Story

    NARCIS (Netherlands)

    Dr. Piet Bakker

    2011-01-01

    Het doel van het project Every Picture Tells a Story is om samen met het werkveld methoden, technieken en kennis te ontwikkelen voor het produceren van effectieve infographics. Dit is nodig omdat de vraag naar infographics in de markt snel toeneemt. Bedrijfsleven en overheden kiezen er steeds vaker

  1. The Picture of Dorian Gray

    NARCIS (Netherlands)

    Wilde, Oscar

    2005-01-01

    On its first publication The Picture of Dorian Gray was regarded as dangerously modern in its depiction of fin-de-sicle decadence. In this updated version of the Faust story, the tempter is Lord Henry Wotton, who lives selfishly for amoral pleasure; Dorian's good angel is the portrait painter Basil

  2. SOFTWARE SUPPORT FOR RICH PICTURES

    DEFF Research Database (Denmark)

    Valente, Andrea; Marchetti, Emanuela

    2010-01-01

    Rich pictures (RP) are common in object-oriented analysis and design courses, but students seem to have problems in integrating them in their projects' workflow. A new software tool is being developed, specific for RP authoring. To better understand students' issues and working practice with RP...

  3. Structuralist readings: Painting vs. picture

    Directory of Open Access Journals (Sweden)

    Marinkov-Pavlović Lidija

    2016-01-01

    Full Text Available The aim of the paper is to point to two fundamentally different strategies of painting practice, that is, to two subsystems of painting: picture and painting. This differentiation can be made within the framework of semiotic and semiological analyses which have developed in theory under the influence of structuralism. The first part of the paper offers a basic insight into the linguistic foundation of structuralistic concept, and then sets a thesis about the possibility of analogue reconceptualisation of semiotics/semiology of painting through Julia Kristeva's semiotics and Roland Barthes' semiology. In addition, it points to the concrete concepts of structural analysis which have accentuated the opposition picture-painting with the examples of art practice concurrent to the development of structuralism. However, what is revealed is that various structuralist readings are significantly subjective to unstable relationship between the basic elements in the pictorial object, that is, in the work of painting.

  4. Structuralist readings: Painting vs. picture

    OpenAIRE

    Marinkov-Pavlović Lidija

    2016-01-01

    The aim of the paper is to point to two fundamentally different strategies of painting practice, that is, to two subsystems of painting: picture and painting. This differentiation can be made within the framework of semiotic and semiological analyses which have developed in theory under the influence of structuralism. The first part of the paper offers a basic insight into the linguistic foundation of structuralistic concept, and then sets a thesis about the possibility of analogue reconceptu...

  5. Strings in the abelized picture

    International Nuclear Information System (INIS)

    Embacher, F.

    1990-01-01

    The transformation properties of the bosonic string variables under the recently discovered abelizing operator are exhibited. The intimate relation of this operator to the light-cone gauge condition is illustrated for the classical string. As an application of the formalism, the derivation of the BRST cohomology by the method of Freemann and Olive is carried over to the abelized picture, where it takes a particularly simple from. (orig.)

  6. Strings in the abelized picture

    International Nuclear Information System (INIS)

    Embacher, F.

    1990-01-01

    The transformation properties of the bosonic string variables under the recently discovered abelizing operator are exhibited. The intimate relation of this operator to the light-cone gauge condition is illustrated for the classical string. As an application of the formalism, the derivation of the BRST cohomology by the method of Freeman and Olive is carried over to the abelized picture, where it takes a particulary simple form. 14 refs. (Author)

  7. Sustainable agriculture in the picture

    International Nuclear Information System (INIS)

    Brouwer, F.M.; De Bont, C.J.A.M.; Leneman, H.; Van der Meulen, H.A.B.

    2004-01-01

    Sustainable agriculture in the picture provides a systematic overview of the available data that are relevant for debate on transitions towards sustainable agriculture. Review for the agrocomplex, greenhouse horticulture, dairy farming and pig farming. Indicators on economy, environment, nature, animal welfare, human and animal health. Results achieved in practice for the three dimensions of sustainable agriculture, namely economics ('profit'), ecology ('planet') and socio-cultural ('people') [nl

  8. Impulsive moving mirror model and the stability of Schroedinger equation with impulse effect in a Banach space

    International Nuclear Information System (INIS)

    Kostadinov, S.I.; Petrov, G.

    1992-01-01

    From a special class of systems has been used a Schroedinger equation with impulse effect in Minkowski space field theory with time dependent boundary conditions, i.e. those of moving mirrors. The field theoretical approach for studying the properties of the vacuum starts from an analysis of the behaviour of local field quantities in Minkowski space with uniformly moving mirrors. For the impulsive moving mirror model is the real process of interaction between the quantum field and the external mirror a subject to disturbances in its evolution acting in time very short compared with the entire duration of the process. So the stability of the solution of the Schroedinger evolution equation for the process in the stability of the vacuum of Casimir. 8 refs

  9. Inverse spectral results for Schroedinger operators on the unit interval with partial information given on the potentials

    International Nuclear Information System (INIS)

    Amour, L.; Raoux, T.; Faupin, J.

    2009-01-01

    We pursue the analysis of the Schroedinger operator on the unit interval in inverse spectral theory initiated in the work of Amour and Raoux [''Inverse spectral results for Schroedinger operators on the unit interval with potentials in Lp spaces,'' Inverse Probl. 23, 2367 (2007)]. While the potentials in the work of Amour and Raoux belong to L 1 with their difference in L p (1≤p k,1 spaces having their difference in W k,p , where 1≤p≤+∞, k(set-membership sign)(0,1,2). It is proved that two potentials in W k,1 ([0,1]) being equal on [a,1] are also equal on [0,1] if their difference belongs to W k,p ([0,a]) and if the number of their common eigenvalues is sufficiently high. Naturally, this number decreases as the parameter a decreases and as the parameters k and p increase

  10. Piecewise linear emulator of the nonlinear Schroedinger equation and the resulting analytic solutions for Bose-Einstein condensates

    International Nuclear Information System (INIS)

    Theodorakis, Stavros

    2003-01-01

    We emulate the cubic term Ψ 3 in the nonlinear Schroedinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a δ function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Ψ 3 one. In particular, it can be used for the nonlinear Schroedinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions

  11. A comparative analysis of Painleve, Lax pair, and similarity transformation methods in obtaining the integrability conditions of nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Al Khawaja, U.

    2010-01-01

    We derive the integrability conditions of nonautonomous nonlinear Schroedinger equations using the Lax pair and similarity transformation methods. We present a comparative analysis of these integrability conditions with those of the Painleve method. We show that while the Painleve integrability conditions restrict the dispersion, nonlinearity, and dissipation/gain coefficients to be space independent and the external potential to be only a quadratic function of position, the Lax Pair and the similarity transformation methods allow for space-dependent coefficients and an external potential that is not restricted to the quadratic form. The integrability conditions of the Painleve method are retrieved as a special case of our general integrability conditions. We also derive the integrability conditions of nonautonomous nonlinear Schroedinger equations for two- and three-spacial dimensions.

  12. A particular inverse problem for Schroedinger discrete equation in two and higher dimensions under apriori information of wave functions

    International Nuclear Information System (INIS)

    Pavlus, M.

    1997-01-01

    The entire potential and the rest of wave functions are determined in parallelepiped domain if the entire discrete spectrum and the apriori information about the wave functions on one side of parallelepiped are given. Formulation for solving the Schroedinger discrete equation in two and higher dimensions is proposed and new formulas are derived for their solution. Two examples for a 2D case and one example for a 3D case are demonstrated

  13. On the Painleve integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Xu Guiqiong; Li Zhibin

    2005-01-01

    It is proven that generalized coupled higher-order nonlinear Schroedinger equations possess the Painleve property for two particular choices of parameters, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests

  14. A Fortran program for the numerical integration of the one-dimensional Schroedinger equation using exponential and Bessel fitting methods

    International Nuclear Information System (INIS)

    Cash, J.R.; Raptis, A.D.; Simos, T.E.

    1990-01-01

    An efficient algorithm is described for the accurate numerical integration of the one-dimensional Schroedinger equation. This algorithm uses a high-order, variable step Runge-Kutta like method in the region where the potential term dominates, and an exponential or Bessel fitted method in the asymptotic region. This approach can be used to compute scattering phase shifts in an efficient and reliable manner. A Fortran program which implements this algorithm is provided and some test results are given. (orig.)

  15. Localized and periodic exact solutions to the nonlinear Schroedinger equation with spatially modulated parameters: Linear and nonlinear lattices

    International Nuclear Information System (INIS)

    Belmonte-Beitia, Juan; Konotop, Vladimir V.; Perez-Garcia, Victor M.; Vekslerchik, Vadym E.

    2009-01-01

    Using similarity transformations we construct explicit solutions of the nonlinear Schroedinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their properties. We put our results in the framework of the exploited perturbation techniques and discuss their implications on the properties of associated linear periodic potentials and on the possibilities of stabilization of gap solitons using polychromatic lattices.

  16. A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schroedinger Equation and Related Problems

    International Nuclear Information System (INIS)

    Anastassi, Z. A.; Simos, T. E.

    2010-01-01

    We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.

  17. De Broglie wavelets versus Schroedinger wave functions: A ribbon model approach to quantum theory and the mechanisms of quantum interference

    Energy Technology Data Exchange (ETDEWEB)

    Tang, Jau

    1996-02-01

    As an alternative to better physical explanations of the mechanisms of quantum interference and the origins of uncertainty broadening, a linear hopping model is proposed with ``color-varying`` dynamics to reflect fast exchange between time-reversed states. Intricate relations between this model, particle-wave dualism, and relativity are discussed. The wave function is shown to possess dual characteristics of a stable, localized ``soliton-like`` de Broglie wavelet and a delocalized, interfering Schroedinger carrier wave function.

  18. Computation of Green function of the Schroedinger-like partial differential equations by the numerical functional integration

    International Nuclear Information System (INIS)

    Lobanov, Yu.Yu.; Shahbagian, R.R.; Zhidkov, E.P.

    1991-01-01

    A new method for numerical solution of the boundary problem for Schroedinger-like partial differential equations in R n is elaborated. The method is based on representation of multidimensional Green function in the form of multiple functional integral and on the use of approximation formulas which are constructed for such integrals. The convergence of approximations to the exact value is proved, the remainder of the formulas is estimated. Method reduces the initial differential problem to quadratures. 16 refs.; 7 tabs

  19. Non-Markovian stochastic Schroedinger equations: Generalization to real-valued noise using quantum-measurement theory

    International Nuclear Information System (INIS)

    Gambetta, Jay; Wiseman, H.M.

    2002-01-01

    Do stochastic Schroedinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system on average obeys a master equation, the answer is yes. Markovian stochastic Schroedinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic Schroedinger equation introduced by Strunz, Diosi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum-measurement theory approach, we rederive their unraveling that involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection, respectively. Although we use quantum-measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction

  20. A Picture of Subsidized Households 2009

    Data.gov (United States)

    Department of Housing and Urban Development — Picture of Subsidized Households describes the nearly 5 million households living in HUD-subsidized housing in the United States for the year 2009. Picture 2009...

  1. Directed forgetting: Comparing pictures and words.

    Science.gov (United States)

    Quinlan, Chelsea K; Taylor, Tracy L; Fawcett, Jonathan M

    2010-03-01

    The authors investigated directed forgetting as a function of the stimulus type (picture, word) presented at study and test. In an item-method directed forgetting task, study items were presented 1 at a time, each followed with equal probability by an instruction to remember or forget. Participants exhibited greater yes-no recognition of remember than forget items for each of the 4 study-test conditions (picture-picture, picture-word, word-word, word-picture). However, this difference was significantly smaller when pictures were studied than when words were studied. This finding demonstrates that the magnitude of the directed forgetting effect can be reduced by high item memorability, such as when the picture superiority effect is operating. This suggests caution in using pictures at study when the goal of an experiment is to examine potential group differences in the magnitude of the directed forgetting effect. 2010 APA, all rights reserved.

  2. The picture superiority effect in associative recognition.

    Science.gov (United States)

    Hockley, William E

    2008-10-01

    The picture superiority effect has been well documented in tests of item recognition and recall. The present study shows that the picture superiority effect extends to associative recognition. In three experiments, students studied lists consisting of random pairs of concrete words and pairs of line drawings; then they discriminated between intact (old) and rearranged (new) pairs of words and pictures at test. The discrimination advantage for pictures over words was seen in a greater hit rate for intact picture pairs, but there was no difference in the false alarm rates for the two types of stimuli. That is, there was no mirror effect. The same pattern of results was found when the test pairs consisted of the verbal labels of the pictures shown at study (Experiment 4), indicating that the hit rate advantage for picture pairs represents an encoding benefit. The results have implications for theories of the picture superiority effect and models of associative recognition.

  3. Use of picture books to explain procedures.

    Science.gov (United States)

    2016-10-06

    A small study conducted at a Swedish hospital on the effect of giving picture books and picture sheets to prepare children for their procedures before and during day surgery is explored in this article.

  4. A Picture of Subsidized Housholds 2008

    Data.gov (United States)

    Department of Housing and Urban Development — Picture of Subsidized Households describes the nearly 5 million households living in HUD-subsidized housing in the United States for the year 2008. Picture 2008...

  5. 77 FR 25082 - Picture Permit Imprint Indicia

    Science.gov (United States)

    2012-04-27

    ... POSTAL SERVICE 39 CFR Part 111 Picture Permit Imprint Indicia AGENCY: Postal Service\\TM\\. ACTION... Service, Domestic Mail Manual (DMM[supreg]) 604.5 to add picture permit imprint indicia standards allowing...: The use of picture permit imprint indicia is designed to improve the effectiveness of a mailpiece by...

  6. Detecting potential ship objects from satellite pictures

    International Nuclear Information System (INIS)

    Luo, B.; Yang, C.C.; Chang, S.K.; Yang, M.C.K.

    1984-01-01

    Heuristic techniques are presented to detect potential ship objects from satellite pictures. These techniques utilize some noise structures of the pixel gray levels, and certain inherent features of a ship in a satellite picture. The scheme has been implemented and successfully tested on SEASAT satellite pictures. A general approach for database-oriented object detection is also suggested

  7. Exploring Multicultural Themes through Picture Books.

    Science.gov (United States)

    Farris, Pamela J.

    1995-01-01

    Advocates inclusion of multicultural picture books in social studies instruction to offer different outlooks and visions in a short format. Describes selection of picture books with multicultural themes and those that represent various cultures, gender equity, and religious themes. Suggests that picture books may help students develop better…

  8. Pictures Improve Memory of SAT Vocabulary Words.

    Science.gov (United States)

    Price, Melva; Finkelstein, Arleen

    1994-01-01

    Suggests that students can improve their memory of Scholastic Aptitude Test vocabulary words by associating the words with corresponding pictures taken from magazines. Finds that long-term recall of words associated with pictures was higher than recall of words not associated with pictures. (RS)

  9. Text-Picture Relations in Cooking Instructions

    NARCIS (Netherlands)

    van der Sluis, Ielka; Leito, Shadira; Redeker, Gisela; Bunt, Harry

    2016-01-01

    Like many other instructions, recipes on packages with ready-to-use ingredients for a dish combine a series of pictures with short text paragraphs. The information presentation in such multimodal instructions can be compact (either text or picture) and/or cohesive (text and picture). In an

  10. Pattern Perception and Pictures for the Blind

    Science.gov (United States)

    Heller, Morton A.; McCarthy, Melissa; Clark, Ashley

    2005-01-01

    This article reviews recent research on perception of tangible pictures in sighted and blind people. Haptic picture naming accuracy is dependent upon familiarity and access to semantic memory, just as in visual recognition. Performance is high when haptic picture recognition tasks do not depend upon semantic memory. Viewpoint matters for the ease…

  11. Inverse scattering transform for the vector nonlinear Schroedinger equation with nonvanishing boundary conditions

    International Nuclear Information System (INIS)

    Prinari, Barbara; Ablowitz, Mark J.; Biondini, Gino

    2006-01-01

    The inverse scattering transform for the vector defocusing nonlinear Schroedinger (NLS) equation with nonvanishing boundary values at infinity is constructed. The direct scattering problem is formulated on a two-sheeted covering of the complex plane. Two out of the six Jost eigenfunctions, however, do not admit an analytic extension on either sheet of the Riemann surface. Therefore, a suitable modification of both the direct and the inverse problem formulations is necessary. On the direct side, this is accomplished by constructing two additional analytic eigenfunctions which are expressed in terms of the adjoint eigenfunctions. The discrete spectrum, bound states and symmetries of the direct problem are then discussed. In the most general situation, a discrete eigenvalue corresponds to a quartet of zeros (poles) of certain scattering data. The inverse scattering problem is formulated in terms of a generalized Riemann-Hilbert (RH) problem in the upper/lower half planes of a suitable uniformization variable. Special soliton solutions are constructed from the poles in the RH problem, and include dark-dark soliton solutions, which have dark solitonic behavior in both components, as well as dark-bright soliton solutions, which have one dark and one bright component. The linear limit is obtained from the RH problem and is shown to correspond to the Fourier transform solution obtained from the linearized vector NLS system

  12. Interpretation of non-Markovian stochastic Schroedinger equations as a hidden-variable theory

    International Nuclear Information System (INIS)

    Gambetta, Jay; Wiseman, H.M.

    2003-01-01

    Do diffusive non-Markovian stochastic Schroedinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function z(t) appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value z(t) even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system 'conditioned' on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit

  13. Inverse periodic problem for the discrete approximation of the Schroedinger nonlinear equation

    International Nuclear Information System (INIS)

    Bogolyubov, N.N.; Prikarpatskij, A.K.; AN Ukrainskoj SSR, Lvov. Inst. Prikladnykh Problem Mekhaniki i Matematiki)

    1982-01-01

    The problem of numerical solution of the Schroedinger nonlinear equation (1) iPSIsub(t) = PSIsub(xx)+-2(PSI)sup(2)PSI. The numerical solution of nonlinear differential equation supposes its discrete approximation is required for the realization of the computer calculation process. Tor the equation (1) there exists the following discrete approximation by variable x(2) iPSIsub(n, t) = (PSIsub(n+1)-2PSIsub(n)+PSIsub(n-1))/(Δx)sup(2)+-(PSIsub(n))sup(2)(PSIsub(n+1)+PSIsub(n-1)), n=0, +-1, +-2... where PSIsub(n)(+) is the corresponding value of PSI(x, t) function in the node and divisions with the equilibrium step Δx. The main problem is obtaining analytically exact solutions of the equations (2). The analysis of the equation system (2) is performed on the base of the discrete analogue of the periodic variant of the inverse scattering problem method developed with the aid of nonlinear equations of the Korteweg-de Vries type. Obtained in explicit form are analytical solutions of the equations system (2). The solutions are expressed through the Riemann THETA-function [ru

  14. Inverting the Rayleigh-Schroedinger perturbation series: Application to atomic stabilization by intense light

    International Nuclear Information System (INIS)

    Baik, M.; Pont, M.; Shakeshaft, R.

    1995-01-01

    We develop a method for calculating the (quasi)energy eigenvalue E(F) of a hydrogen atom in a nonperturbative ac field of strength F starting from a knowledge of the coefficients E (2m) of the Rayleigh-Schroedinger perturbation series E(F)=tsum m=0 M E (2m) F 2m . We first use the coefficients E (2m) (the unperturbed energy is E (0) ) to construct the inverse series F 2 (E)=tsum m=1 M F (m) (E-E (0) ) m . We resum the latter series using the Pade method, and solve the implicit equation F 2 (E)=bar F 2 for E(bar F). The reconstructed function E(F) has the singularity structure appropriate to the true E(F). We are able to obtain good results for the lifetime of a hydrogen atom in a high-frequency field up to very high intensities, well into the (highly nonperturbative) stabilization regime

  15. Concept of a collective subspace associated with the invariance principle of the Schroedinger equation

    International Nuclear Information System (INIS)

    Marumori, Toshio; Hayashi, Akihisa; Tomoda, Toshiaki; Kuriyama, Atsushi; Maskawa, Toshihide

    1980-01-01

    The aim of this series of papers is to propose a microscopic theory to go beyond the situations where collective motions are described by the random phase approximation, i.e., by small amplitude harmonic oscillations about equilibrium. The theory is thus appropriate for the microscopic description of the large amplitude collective motion of soft nuclei. The essential idea is to develop a method to determine the collective subspace (or submanifold) in the many-particle Hilbert space in an optimal way, on the basis of a fundamental principle called the invariance principle of the Schroedinger equation. By using the principle within the framework of the Hartree-Fock theory, it is shown that the theory can clarify the structure of the so-called ''phonon-bands'' by self-consistently deriving the collective Hamiltonian where the number of the ''physical phonon'' is conserved. The purpose of this paper is not to go into detailed quantitative discussion, but rather to develop the basic idea. (author)

  16. Variational method for the derivative nonlinear Schroedinger equation with computational applications

    Energy Technology Data Exchange (ETDEWEB)

    Helal, M A [Mathematics Department, Faculty of Science, Cairo University (Egypt); Seadawy, A R [Mathematics Department, Faculty of Science, Beni-Suef University (Egypt)], E-mail: mahelal@yahoo.com, E-mail: aly742001@yahoo.com

    2009-09-15

    The derivative nonlinear Schroedinger equation (DNLSE) arises as a physical model for ultra-short pulse propagation. In this paper, the existence of a Lagrangian and the invariant variational principle (i.e. in the sense of the inverse problem of calculus of variations through deriving the functional integral corresponding to a given coupled nonlinear partial differential equations) for two-coupled equations describing the nonlinear evolution of the Alfven wave with magnetosonic waves at a much larger scale are given and the functional integral corresponding to those equations is derived. We found the solutions of DNLSE by choice of a trial function in a region of a rectangular box in two cases, and using this trial function, we find the functional integral and the Lagrangian of the system without loss. Solution of the general case for the two-box potential can be obtained on the basis of a different ansatz where we approximate the Jost function using polynomials of order n instead of the piecewise linear function. An example for the third order is given for illustrating the general case.

  17. The effective Schroedinger equation of the optical model of composite nuclei elastic collisions

    International Nuclear Information System (INIS)

    Mondragon, A.; Hernandez, E.

    1980-01-01

    An effective hamiltonian for elastic collisions between composite nuclei is obtained from the Schroedinger equation of the complete many-body system and its fully antisymmetric wave functions by means of a projection operator technique. This effective hamiltonian, defined in such a way that it has to reproduce the scattering amplitude in full detail, including exchange effects, is explicitly Galilean invariant. The effective interaction operator is a function of the relative distance between the centers of mass of the colliding nuclei and the constants of the motion of the whole system. The interaction operator of the optical model is obtained next, requiring as usual, that it reproduces the average over the energy of the scattering amplitude and keeping the Galilean invariance. The resulting optical potential operator has some terms identical to those obtained in the Resonating Group Method, and others coming from the elimination of all non elastic channels and the delayed elastic scattering. This result makes the relation existing among the projection operator method to the Feshbach and the cluster model equations of motion for positive energies (RGM) explicit. The additional interaction terms due to the flux loss in the elastic channel are non-local, and non-hermitean operators expressed in terms of the transition amplitudes and the density of states of the compound nucleus in such a way that an approximate evaluation, in a systematic fashion, seems possible. Theangular momentum dependence of the optical potential operator is discussed in some detail. (author)

  18. Excitation of multiphase waves of the nonlinear Schroedinger equation by capture into resonances

    International Nuclear Information System (INIS)

    Friedland, L.; Shagalov, A.G.

    2005-01-01

    A method for adiabatic excitation and control of multiphase (N-band) waves of the periodic nonlinear Schroedinger (NLS) equation is developed. The approach is based on capturing the system into successive resonances with external, small amplitude plane waves having slowly varying frequencies. The excitation proceeds from zero and develops in stages, as an (N+1)-band (N=0,1,2,...), growing amplitude wave is formed in the (N+1)th stage from an N-band solution excited in the preceding stage. The method is illustrated in simulations, where the excited multiphase waves are analyzed via the spectral approach of the inverse scattering transform method. The theory of excitation of 0- and 1-band NLS solutions by capture into resonances is developed on the basis of a weakly nonlinear version of Whitham's averaged variational principle. The phenomenon of thresholds on the driving amplitudes for capture into successive resonances and the stability of driven, phase-locked solutions in these cases are discussed

  19. The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schroedinger form

    International Nuclear Information System (INIS)

    Mourad, J.; Sazdjian, H.

    1994-01-01

    The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the 4x4 matrix wave function in terms of one of the 2x2 components, to a single equation of the Pauli-Schroedinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two-component form of the one-particle Dirac equation with external static potentials. The Hamiltonian, to order 1/c 2 , reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order 1/c 2 , corresponding to confining scalar potentials, is displayed. (authors). 32 refs., 2 figs

  20. Stationary localized modes of the quintic nonlinear Schroedinger equation with a periodic potential

    International Nuclear Information System (INIS)

    Alfimov, G. L.; Konotop, V. V.; Pacciani, P.

    2007-01-01

    We consider localized modes (bright solitons) of the one-dimensional quintic nonlinear Schroedinger equation with a periodic potential, describing several mean-field models of low-dimensional condensed gases. In the case of attractive nonlinearity we deduce sufficient conditions for collapse. We show that there exist spatially localized modes with arbitrarily large numbers of particles. We study such solutions in the semi-infinite gap (attractive case) and in the first gap (attractive and repulsive cases), and show that a nonzero minimum value of the number of particles is necessary for a localized mode to be created. In the limit of large negative frequencies (attractive case) we observe quantization of the number of particles of the stationary modes. Such solutions can be interpreted as coupled Townes solitons and appear to be stable. The modes in the first gap have numbers of particles infinitely growing with frequencies approaching one of the gap edges, which is explained by the power decay of the modes. Stability of the localized modes is discussed

  1. Non-negative Feynman endash Kac kernels in Schroedinger close-quote s interpolation problem

    International Nuclear Information System (INIS)

    Blanchard, P.; Garbaczewski, P.; Olkiewicz, R.

    1997-01-01

    The local formulations of the Markovian interpolating dynamics, which is constrained by the prescribed input-output statistics data, usually utilize strictly positive Feynman endash Kac kernels. This implies that the related Markov diffusion processes admit vanishing probability densities only at the boundaries of the spatial volume confining the process. We discuss an extension of the framework to encompass singular potentials and associated non-negative Feynman endash Kac-type kernels. It allows us to deal with a class of continuous interpolations admitted by general non-negative solutions of the Schroedinger boundary data problem. The resulting nonstationary stochastic processes are capable of both developing and destroying nodes (zeros) of probability densities in the course of their evolution, also away from the spatial boundaries. This observation conforms with the general mathematical theory (due to M. Nagasawa and R. Aebi) that is based on the notion of multiplicative functionals, extending in turn the well known Doob close-quote s h-transformation technique. In view of emphasizing the role of the theory of non-negative solutions of parabolic partial differential equations and the link with open-quotes Wiener exclusionclose quotes techniques used to evaluate certain Wiener functionals, we give an alternative insight into the issue, that opens a transparent route towards applications.copyright 1997 American Institute of Physics

  2. Electron confinement in quantum nanostructures: Self-consistent Poisson-Schroedinger theory

    International Nuclear Information System (INIS)

    Luscombe, J.H.; Bouchard, A.M.; Luban, M.

    1992-01-01

    We compute the self-consistent electron states and confining potential, V(r,T), for laterally confined cylindrical quantum wires at a temperature T from a numerical solution of the coupled Poisson and Schroedinger (PS) equations. Finite-temperature effects are included in the electron density function, n(r,T), via the single-particle density matrix in the grand-canonical ensemble using the self-consistent bound states. We compare our results for a GaAs quantum wire with those obtained previously [J. H. Luscombe and M. Luban, Appl. Phys. Lett. 57, 61 (1990)] from a finite-temperature Thomas-Fermi (TF) approximation. We find that the TF results agree well with those of the more realistic, but also more computationally intensive PS theory, except for low temperatures or for cases where the quantum wire is almost, but not totally, depleted due to a combination of either small geometry, surface boundary conditions, or low doping concentrations. In the latter situations, the number of subbands that are populated is relatively small, and both n(r,T) and V(r,T) exhibit Friedel-type oscillations. Otherwise the TF theory, which is based on free-particle states, is remarkably accurate. We also present results for the partial electron density functions associated with the angular momentum quantum numbers, and discuss their role in populating the quantum wire

  3. Bound State Eigenvalues of the Schroedinger Eq. in two Spatial Variables.

    Science.gov (United States)

    Rawitscher, George H.; Koltracht, Israel

    2002-08-01

    An efficient spectral integral equation method (SIEM) has recently been developed for obtaining the scattering solution of a one-dimensional Schroedinger equation.(R.A. Gonzales, S.-Y. Kang, I. Koltracht and G. Rawitscher, J. of Comput. Phys. 153, 160 (1999).) The purpose of the present study is to extend this method to the case of bound-states in more than one dimension. Even though other methods have already been developed for this case, such as finite element methods, the application we have in mind is to solve the non-linear Bose-Einstein condensate case in the presence of an optical lattice. In the presence of a trapping potential alone, a B-E condensate solution has been obtained by a new iterative spectral method which solves the differential equation.(Y.-S. Choi, J. Javanainen, I. Koltracht, M. Koš)trun, P.J. McKenna and N. Savytska "A Fast Algorithm for the Solution of the Time-Independent Gross-Pitaevskii Equation," Submitted to Computational Physics. But this method becomes inadequate for the case that several potential barriers are also present. The reason that the SIEM is expected to be better suited is that it distributes the collocation points much more efficiently into partitions of variable size.

  4. Phase integral approximation for coupled ordinary differential equations of the Schroedinger type

    International Nuclear Information System (INIS)

    Skorupski, Andrzej A.

    2008-01-01

    Four generalizations of the phase integral approximation (PIA) to sets of ordinary differential equations of Schroedinger type [u j '' (x)+Σ k=1 N R jk (x)u k (x)=0, j=1,2,...,N] are described. The recurrence relations for higher order corrections are given in a form valid to arbitrary order and for the matrix R(x)[≡(R jk (x))] either Hermitian or non-Hermitian. For Hermitian and negative definite R(x) matrices, a Wronskian conserving PIA theory is formulated, which generalizes Fulling's current conserving theory pertinent to positive definite R(x) matrices. The idea of a modification of the PIA, which is well known for one equation [u '' (x)+R(x)u(x)=0], is generalized to sets. A simplification of Wronskian or current conserving theories is proposed which in each order eliminates one integration from the formulas for higher order corrections. If the PIA is generated by a nondegenerate eigenvalue of the R(x) matrix, the eliminated integration is the only one present. In that case, the simplified theory becomes fully algorithmic and is generalized to non-Hermitian R(x) matrices. The general theory is illustrated by a few examples automatically generated by using the author's program in MATHEMATICA published in e-print arXiv:0710.5406 [math-ph

  5. Exact perturbation theory of multiphoton processes at high intensities. [Schroedinger equation, perturbation theory, matrix

    Energy Technology Data Exchange (ETDEWEB)

    Faisal, F H.M. [Bielefeld Univ. (Germany, F.R.). Fakultaet fuer Physik

    1976-06-11

    In this work the perturbation theory for multiphoton processes at high intensities is investigated and it is described an analytical method of summing the perturbation series to extract the contribution from all terms that give rise to the absorption of N photons by an atomic system. The method is first applied to the solution of a simple model problem and the result is confirmed by direct integration of the model Schroedinger equation. The usual lowest (nonvanishing)-order perturbation-theoretical calculation is also carried out for this model to demonstrate explicitly that the full result correctly reproduces that of the lowest-order theory in the limit of low intensity. The method is then extended to the case of an atomic system with well-developed spectrum (e.g. H atom) and the N-photon T-matrix is derived in terms of a ''photon matrix'' asub(N), for which a three-term recurrence relation is established. Next, from the vantage point of the general result obtained here, A probe is made into the nature of several approximate nonperturbative solutions that have appeared in the literature in the past. It is shown here that their applicability is severely restricted by the requirement of the essential spectral degeneracy of the atomic system. Finally, appendix A outlines a prescription of computing the photon matrix asub(N), which (as in the usual lowest-order perturbation-theoretical calculation)requires a knowledge of the eigenfunctions and eigenvalues of the atomic Hamiltonian only.

  6. Cascaded Processing in Written Naming: Evidence from the Picture-Picture Interference Paradigm

    Science.gov (United States)

    Roux, Sebastien; Bonin, Patrick

    2012-01-01

    The issue of how information flows within the lexical system in written naming was investigated in five experiments. In Experiment 1, participants named target pictures that were accompanied by context pictures having phonologically and orthographically related or unrelated names (e.g., a picture of a "ball" superimposed on a picture of…

  7. Different Loci of Semantic Interference in Picture Naming vs. Word-Picture Matching Tasks

    OpenAIRE

    Harvey, Denise Y.; Schnur, Tatiana T.

    2016-01-01

    Naming pictures and matching words to pictures belonging to the same semantic category impairs performance relative to when stimuli come from different semantic categories (i.e., semantic interference). Despite similar semantic interference phenomena in both picture naming and word-picture matching tasks, the locus of interference has been attributed to different levels of the language system – lexical in naming and semantic in word-picture matching. Although both tasks involve access to shar...

  8. Picture chamber for radiographic system

    International Nuclear Information System (INIS)

    1977-01-01

    The picture chamber for a radiographic system is characterised by a base, a first electrode carried in the base, an X-ray irradiation window provided with an outer plate and an inner plate and a conducting surface which serves as a second electrode, which has a plate gripping it at each adjacent edge and which has at the sides a space which is occupied by a filling material, maintained at a steady pressure, by means of the mounting against the base and wherein the inner plate lies against the first electrode and which is provided with a split, and with means for the separation of the split in the area of the inner plate so that a fluid may be retained in the split. (G.C.)

  9. The Analytic Solution of Schroedinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

    International Nuclear Information System (INIS)

    Hu Xianquan; Luo Guang; Cui Lipeng; Niu Lianbin; Li Fangyu

    2009-01-01

    The analytic solution of the radial Schroedinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schroedinger equation is V(r) = α 1 r 8 + α 2 r 3 + α 3 r 2 + β 3 r -1 + β 2 r -3 + β 1 r -4 . Generally speaking, there is only an approximate solution, but not analytic solution for Schroedinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schroedinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schroedinger equation; and lastly, they discuss the solutions and make conclusions. (general)

  10. Manipulating affective state using extended picture presentations.

    Science.gov (United States)

    Sutton, S K; Davidson, R J; Donzella, B; Irwin, W; Dottl, D A

    1997-03-01

    Separate, extended series of positive, negative, and neutral pictures were presented to 24 (12 men, 12 women) undergraduates. Each series was presented on a different day, with full counterbalancing of presentation orders. Affective state was measured using (a) orbicularis oculi activity in response to acoustic startle probes during picture presentation, (b) corrugator supercilii activity between and during picture presentation, and (c) changes in self-reports of positive and negative affect. Participants exhibited larger eyeblink reflex magnitudes when viewing negative than when viewing positive pictures. Corrugator activity was also greater during the negative than during the positive picture set, during both picture presentation and the period between pictures. Self-reports of negative affect increased in response to the negative picture set, and self-reports of positive affect were greatest following the positive picture set. These findings suggest that extended picture presentation is an effective method of manipulating affective state and further highlight the utility of startle probe and facial electromyographic measures in providing on-line readouts of affective state.

  11. Frozen and broken color: a matrix Schroedinger equation in the semiclassical limit

    International Nuclear Information System (INIS)

    Orbach, H.S.

    1981-01-01

    We consider the case of frozen color, i.e, where global color symmetry remains exact, but where colored states have a mass large compared to color-singlet mesons. Using semiclassical WKB formalism, we construct the spectrum of bound states. In order to determine the charge of the constituents, we then consider deep-inelastic scattering of an external probe (e.g., lepton) from our one-dimensional meson. We calculate explicitly the structure function, W, in the WKB limit and show how Lipkin's mechanism is manifested, as well as how scaling behavior comes. We derive the WKB formalism as a special case of a method of obtaining WKB type solutions for generalized Schroedinger equations for which the Hamiltonian is an arbitrary matrix function of any number of pairs of canonical operators. We generalize these considerations to the case of broken color symmetry - but where the breaking is not so strong as to allow low-lying states to have a large amount of mixing with the colored states. In this case, the degeneracy of excited colored states can be broken. We find that local excitation of color guarantees global excitation of color; i.e., if at a given energy colored semiclassical states can be constructed with size comparable to that of the ground state wave function, colored states of that energy will also exist in the spectrum of the full theory and will be observed. However, global existence of color does not guarantee the excitation of colored states via deep-inelastic processes

  12. Two routes to the one-dimensional discrete nonpolynomial Schroedinger equation

    International Nuclear Information System (INIS)

    Gligoric, G.; Hadzievski, Lj.; Maluckov, A.; Salasnich, L.; Malomed, B. A.

    2009-01-01

    The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schroedinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce 'model 1' (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. 'Model 2,' which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2--in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.

  13. Single particle Schroedinger fluid and moments of inertia of deformed nuclei

    International Nuclear Information System (INIS)

    Doma, S.B.

    2002-01-01

    The authors have applied the theory of the single-particle Schroedinger fluid to the nuclear collective motion of axially deformed nuclei. A counter example of an arbitrary number of independent nucleons in the anisotropic harmonic oscillator potential at the equilibrium deformation has been also given. Moreover, the ground states of the doubly even nuclei in the s-d shell 20 Ne, 24 Mg, 28 Si, 32 S and 36 Ar are constructed by filling the single-particle states corresponding to the possible values of the number of quanta of excitations n x , n y and n z . Accordingly, the cranking-model, the rigid-body model and the equilibrium-model moments of inertia of these nuclei are calculated as functions of the oscillator parameters ℎω x , ℎω y and ℎω z which are given in terms of the non deformed value ℎω 0 0 , depending on the mass number A, the number of neutrons N, the number of protons Z, and the deformation parameter β. The calculated values of the cranking-model moments of inertia of these nuclei are in good agreement with the corresponding experiential values and show that the considered axially deformed nuclei may have oblate as well as prolate shapes and that the nucleus 24 Mg is the only one which is highly deformed. The rigid-body model and the equilibrium-model moments of inertia of the two nuclei 20 Ne and 24 Mg are also in good agreement with the corresponding experimental values

  14. Wigner method dynamics in the interaction picture

    DEFF Research Database (Denmark)

    Møller, Klaus Braagaard; Dahl, Jens Peder; Henriksen, Niels Engholm

    1994-01-01

    that the dynamics of the interaction picture Wigner function is solved by running a swarm of trajectories in the classical interaction picture introduced previously in the literature. Solving the Wigner method dynamics of collision processes in the interaction picture ensures that the calculated transition......The possibility of introducing an interaction picture in the semiclassical Wigner method is investigated. This is done with an interaction Picture description of the density operator dynamics as starting point. We show that the dynamics of the density operator dynamics as starting point. We show...... probabilities are unambiguous even when the asymptotic potentials are anharmonic. An application of the interaction picture Wigner method to a Morse oscillator interacting with a laser field is presented. The calculated transition probabilities are in good agreement with results obtained by a numerical...

  15. Emotionally Negative Pictures Enhance Gist Memory

    OpenAIRE

    Bookbinder, S. H.; Brainerd, C. J.

    2016-01-01

    In prior work on how true and false memory are influenced by emotion, valence and arousal have often been conflated. Thus, it is difficult to say which specific effects are due to valence and which are due to arousal. In the present research, we used a picture-memory paradigm that allowed emotional valence to be manipulated with arousal held constant. Negatively-valenced pictures elevated both true and false memory, relative to positive and neutral pictures. Conjoint recognition modeling reve...

  16. A limit of the confluent Heun equation and the Schroedinger equation for an inverted potential and for an electric dipole

    International Nuclear Information System (INIS)

    El-Jaick, Lea Jaccoud; Figueiredo, Bartolomeu D.B.

    2009-01-01

    We reexamine and extend a group of solutions in series of Bessel functions for a limiting case of the confluent Heun equation and, then, apply such solutions to the one-dimensional Schroedinger equation with an inverted quasi-exactly solvable potential as well as to the angular equation for an electron in the field of a point electric dipole. For the first problem we find finite and infinite-series solutions which are convergent and bounded for any value of the independent variable. For the angular equation, we also find expansions in series of Jacobi polynomials. (author)

  17. Variational principles for collective motion: Relation between invariance principle of the Schroedinger equation and the trace variational principle

    International Nuclear Information System (INIS)

    Klein, A.; Tanabe, K.

    1984-01-01

    The invariance principle of the Schroedinger equation provides a basis for theories of collective motion with the help of the time-dependent variational principle. It is formulated here with maximum generality, requiring only the motion of intrinsic state in the collective space. Special cases arise when the trial vector is a generalized coherent state and when it is a uniform superposition of collective eigenstates. The latter example yields variational principles uncovered previously only within the framework of the equations of motion method. (orig.)

  18. Spectral fitting method for the solution of time-dependent Schroedinger equations: Applications to atoms in intense laser fields

    International Nuclear Information System (INIS)

    Qiao Haoxue; Cai Qingyu; Rao Jianguo; Li Baiwen

    2002-01-01

    A spectral fitting method for solving the time-dependent Schroedinger equation has been developed and applied to the atom in intense laser fields. This method allows us to obtain a highly accurate time-dependent wave function with a contribution from the high-order term of Δt. Moreover, the time-dependent wave function is determined on a small number of discrete mesh points, thus making calculations simple and accurate. This method is illustrated by computing wave functions and harmonic generation spectra of a model atom in laser fields

  19. Born series for (2 cluster) → (2 cluster) scattering of two, three, and four particle Schroedinger operators

    International Nuclear Information System (INIS)

    Hagedorn, G.A.

    1979-01-01

    We investigate elastic and inelastic (2 cluster)→(2 cluster)scattering for classes of two, three, and four body Schroedinger operators H=H 0 +ΣVij. Formulas are derived for those generalized eigenfunctions of H which correspond asymptotically in the past to two freely moving clusters. With these eigenfunctions, we establish a formula for the (2 cluster)→(2 cluster) T-matrix and prove the convergence of a Born series for the T-matrix at high energy. (orig.) [de

  20. Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schroedinger problem and the KPI equation

    International Nuclear Information System (INIS)

    Boiti, M.; Pempinelli, F.; Pogrebkov, A.K.; Polivanov, M.C.

    1993-01-01

    The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. The authors demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schroedinger equation as an example, it is shown that all types of solutions of the linear problem, as well as spectral data known in the literature, are given as specific values of this unique function - the resolvent function. A new form of the inverse problem is formulated. 7 refs

  1. Selected pictures of the month

    CERN Multimedia

    Claudia Marcelloni de Oliveira

    View of a single MDT Big Wheel (on side A in UX15 cavern) taken during its last movement immediately after being assembled and just before being connected to the neighbouring TGC1 wheel. Assembly work on the Cathode Strip Chambers on Small Wheel C in building 190. Connecting the services for the Cathode Strip Chambers. The installation of the optical fibers for the readout of the Cathode Strip Chambers on Small Weel C by the Irvine group. Best from our archives: View of the End Cap Calorimeter and TGC big wheel from the Cryostat side A of ATLAS cavern taken on 22 May 2007. The picture above was taken from the platform in the middle, between the Cryostat and the End-Cap. Muriel hopes you all had a great vacation. She herself had a wonderful time sailing in Galicia (North Western Spain). She can be seen here wearing the traditional dress offered to her by "Los Amigos de las Dornas" (Friends of the Dornas -traditional sailing boats used for fishing) - when she became ...

  2. Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schroedinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

    International Nuclear Information System (INIS)

    Keanini, R.G.

    2011-01-01

    Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the

  3. On the reduction of the multidimensional stationary Schroedinger equation to a first-order equation and its relation to the pseudoanalytic function theory

    Energy Technology Data Exchange (ETDEWEB)

    Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)

    2005-01-28

    Given a particular solution of a one-dimensional stationary Schroedinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schroedinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schroedinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schroedinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schroedinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schroedinger equation. Moreover, for an ample

  4. Christians in South Africa: The statistical picture

    African Journals Online (AJOL)

    Abstract. Christians in South Africa; The statistical picture. Government censuses since 1960 indicate that the religious picture was already largely fixed by the 1950s. Already at that stage some 3 out of 4. South Africans identified themselves as 'Christians'. Since then this percentage grew steadily, mainly because of ...

  5. Picture Books and the Art of Collage.

    Science.gov (United States)

    Prudhoe, Catherine M.

    2003-01-01

    Explores how teachers can use picture book illustrations to teach children the art of collage. Focuses on three children's picture books and offers art activities showcasing three collage techniques: (1) cut and torn paper collage; (2) photomontage; and (3) texture collages and collage constructions. Relates each activity to the National Standards…

  6. Algorithms for coding scanned halftone pictures

    DEFF Research Database (Denmark)

    Forchhammer, Søren; Forchhammer, Morten

    1988-01-01

    A method for coding scanned documents containing halftone pictures, e.g. newspapers and magazines, for transmission purposes is proposed. The halftone screen is estimated and the grey value of each dot is found, thus giving a compact description. At the receiver the picture is rescreened. A novel...

  7. The Picture Superiority Effect and Biological Education.

    Science.gov (United States)

    Reid, D. J.

    1984-01-01

    Discusses learning behaviors where the "picture superiority effect" (PSE) seems to be most effective in biology education. Also considers research methodology and suggests a new research model which allows a more direct examination of the strategies learners use when matching up picture and text in efforts to "understand"…

  8. Positioning Picture Books within the Mathematics Curriculum

    Science.gov (United States)

    Jenkins, Kate

    2010-01-01

    Most teachers feel confident espousing the benefits of using picture books in English lessons, talking about the importance of using the illustrations to enhance the text, engaging students and fostering a love and appreciation of literature. How many teachers passionately advocate the use of these same picture books in mathematics lessons? This…

  9. The Untapped Potential of Picture Books

    Science.gov (United States)

    Hager, Stephanie

    2015-01-01

    This article discusses the role picture books play in helping young writers. Third-grade students were read engaging picture books for the sole purpose of noticing and naming different features they encountered during the read-alouds. Students were able to recognize the tools many authors and illustrators use such as onomatopoeia, varied font…

  10. Magazine Picture Collage in Group Supervision

    Science.gov (United States)

    Shepard, Blythe C.; Guenette, Francis L.

    2010-01-01

    A magazine picture collage activity was used with three female counsellor education students as a vehicle to support them in processing their experience as counsellors in training. The use of magazine picture collage in group supervision is described, and the benefits and challenges are presented. The collages served as jumping-off points for…

  11. Gender Stereotypes in Children's Picture Books.

    Science.gov (United States)

    Narahara, May M.

    Research has examined how gender stereotypes and sexism in picture books affect the development of gender identity in young children, how children's books in the last decade have portrayed gender, and how researchers evaluate picture books for misrepresentations of gender. A review of the research indicated that gender development is a critical…

  12. Picture Books Peek behind Cultural Curtains.

    Science.gov (United States)

    Marantz, Sylvia; Marantz, Kenneth

    2000-01-01

    Discusses culture in picture books in three general categories: legends and histories; current life in particular areas; and the immigrant experience. Considers the translation of visual images, discusses authentic interpretations, and presents an annotated bibliography of picture books showing cultural diversity including African, Asian, Mexican,…

  13. Rapid induction of false memory for pictures.

    Science.gov (United States)

    Weinstein, Yana; Shanks, David R

    2010-07-01

    Recognition of pictures is typically extremely accurate, and it is thus unclear whether the reconstructive nature of memory can yield substantial false recognition of highly individuated stimuli. A procedure for the rapid induction of false memories for distinctive colour photographs is proposed. Participants studied a set of object pictures followed by a list of words naming those objects, but embedded in the list were names of unseen objects. When subsequently shown full colour pictures of these unseen objects, participants consistently claimed that they had seen them, while discriminating with high accuracy between studied pictures and new pictures whose names did not appear in the misleading word list. These false memories can be reported with high confidence as well as the feeling of recollection. This new procedure allows the investigation of factors that influence false memory reports with ecologically valid stimuli and of the similarities and differences between true and false memories.

  14. The Geneva Smoking Pictures: development and preliminary validation.

    OpenAIRE

    Khazaal, Yasser; Zullino, Daniele; Billieux, Joël

    2012-01-01

    Cue reactivity is essential to the maintenance of addictive disorders. A useful way to study cue reactivity is by means of normative pictures, but few validated tobacco-related pictures are available. This study describes a database of smoking-related pictures: The Geneva Smoking Pictures (GSP). Sixty smoking-related pictures were presented to 91 participants who assessed them according to the classic emotional pictures validation provided by the International Affective Picture System (NIMH C...

  15. On the classical theory of ordinary linear differential equations of the second order and the Schroedinger equation for power law potentials

    International Nuclear Information System (INIS)

    Lima, M.L.; Mignaco, J.A.

    1983-01-01

    The power law potentials in the Schroedinger equation solved recently are shown to come from the classical treatment of the singularities of a linear, second order differential equation. This allows to enlarge the class of solvable power law potentials. (Author) [pt

  16. Erwin Schroedinger's views on gravitational physics during his last years at the University of Vienna and some research ensuing from it

    International Nuclear Information System (INIS)

    Halpern, L.

    1987-01-01

    The author, who was Schroedinger's assistant during his last years in Vienna, gives an account of Schroedinger's views and activities during that time which lead him to a different approach to research on the relations between gravitation and quantum phenomena. Various features of past research are outlined in nontechnical terms. A heuristic argument is presented for the role of the zero-point energy of massive particles in counteracting gravitational collapse and the formation of horizons. Arguments are presented for the view that progress in describing extreme gravitational phenomena can be achieved by the new outlook obtained from the introduction of the analog of Maxwell's vacuum displacement term with a quasiconstant parameter, rather than from renormalization of special processes, even if this is successful. The results can be expected to be in accord with Schroedinger's conjectures. A physical interpretation for the change of sign of the differential invariant of Karlhede, Lindstroem, and Aman at the horizon is suggested. Some important historical details about Schroedinger are touched upon

  17. Comment on: Path integral solution of the Schroedinger equation in curvilinear coordinates: A straightforward procedure [J. Math. Phys. 37, 4310 endash 4319 (1996)

    International Nuclear Information System (INIS)

    Wurm, A.; LaChapelle, J.

    1997-01-01

    The authors comment on the paper by J. LaChapelle, J. Math. Phys. 37, 4310 (1996), and give explicit expressions for the parametrization, its solution, and the Lie derivatives of the Schroedinger equation for the case of n-dimensional spherical coordinates

  18. Use of time-dependent Schroedinger equation to analyze effect of collectivization of valence neutrons on near-barrier nuclear fusion enhancement

    International Nuclear Information System (INIS)

    Zagrebaev, V.I.; ); Samarin, V.V.

    2006-01-01

    Fusion of heavy nuclei was analyzed on the basis of the numerical solution of the Schroedinger three-body and three-dimensional nonstationary equations. One revealed the increase of fuss ion probability in 66 He + 2O Pb reaction caused by transfer and collectivization of valent neutrons [ru

  19. On the solution of the inverse scattering problem for the quadratic bundle of the one-dimensional Schroedinger operators of the whole axis

    International Nuclear Information System (INIS)

    Maksudov, F.G.; Gusejnov, G.Sh.

    1986-01-01

    Inverse scattering problem for the quadratic bundle of the Schroedinger one-dimensional operators in the whole axis is solved. The problem solution is given on the assumption of the discrete spectrum absence. In the discrete spectrum presence the inverse scattering problem solution is known for the Shroedinger differential equation considered

  20. Picture archiving and communications system EFPACS series

    International Nuclear Information System (INIS)

    Hirasawa, Teiji; Mukasa, Minoru; Hiramatsu, Jun-ichi

    1989-01-01

    Fuji EFPACS (Effective Fuji PACS) is a picture archiving and communications system which efficiently executes centralized management of quantities of image data produced in a hospital. Main features of this system are high-speed retrieval and display function resulting from high-grade imaging technology. This system also strongly supports picture management for multi-modalities, picture storage, and education. EFPACS-500 and EFPACS-1000 series are available according to a system scale. An optimal system configuration can be obtained in a building-up style. This paper describes the features and performance of the EFPACS. (author)

  1. Irreducible Brillouin conditions and contracted Schroedinger equations for n-electron systems. IV. Perturbative analysis

    International Nuclear Information System (INIS)

    Kutzelnigg, Werner; Mukherjee, Debashis

    2004-01-01

    The k-particle irreducible Brillouin conditions IBC k and the k-particle irreducible contracted Schroedinger equations ICSE k for a closed-shell state are analyzed in terms of a Moeller-Plesset-type perturbation expansion. The zeroth order is Hartree-Fock. From the IBC 2 (1) , i.e., from the two-particle IBC to first order in the perturbation parameter μ, one gets the leading correction λ 2 (1) to the two-particle cumulant λ 2 correctly. However, in order to construct the second-order energy E 2 , one also needs the second-order diagonal correction γ D (2) to the one-particle density matrix γ. This can be obtained: (i) from the idempotency of the n-particle density matrix, i.e., essentially from the requirement of n-representability; (ii) from the ICSE 1 (2) ; or (iii) by means of perturbation theory via a unitary transformation in Fock space. Method (ii) is very unsatisfactory, because one must first solve the ICSE 3 (2) to get λ 3 (2) , which is needed in the ICSE 2 (2) to get λ 2 (2) , which, in turn, is needed in the ICSE 1 (2) to get γ (2) . Generally the (k+1)-particle approximation is needed to obtain E k correctly. One gains something, if one replaces the standard hierarchy, in which one solves the ICSE k , ignoring λ k+1 and λ k+2 , by a renormalized hierarchy, in which only λ k+2 is ignored, and λ k+1 is expressed in terms of the λ p of lower particle rank via the partial trace relation for λ k+2 . Then the k-particle approximation is needed to obtain E k correctly. This is still poorer than coupled-cluster theory, where the k-particle approximation yields E k+1 . We also study the possibility to use some simple necessary n-representability conditions, based on the non-negativity of γ (2) and two related matrices, in order to get estimates for γ D (2) in terms of λ 2 (1) . In general these estimates are rather weak, but they can become close to the best possible bounds in special situations characterized by a very sparse structure of λ 2

  2. NIH Abroad: Pictures Are Crowd Pullers

    Science.gov (United States)

    ... turn Javascript on. "Pictures Are Crowd Pullers …" Art, culture, and the Internet combine to intervene against malaria ... Not ripe mangoes. Not witchcraft. The images and words, which speak directly to local beliefs in villages ...

  3. Interframe transform coding of picture data

    Science.gov (United States)

    Ahmed, N.; Natarajan, T. R.

    1976-01-01

    This semi-tutorial paper describes the process of using orthogonal transforms for the purposes of encoding TV picture data. Results pertaining to a 6:1 data compression experiment using the Walsh-Hadamard transform are included.

  4. Pattern Perception and Pictures for the Blind

    Directory of Open Access Journals (Sweden)

    Melissa McCarthy

    2005-01-01

    Full Text Available This article reviews recent research on perception of tangible pictures in sighted and blind people. Haptic picture naming accuracy is dependent upon familiarity and access to semantic memory, just as in visual recognition. Performance is high when haptic picture recognition tasks do not depend upon semantic memory. Viewpoint matters for the ease or difficulty of interpreting haptic pictures of solid objects. Top views were easiest for sighted and blind persons when geometrical solids had constant crosssections in the vertical axis. The presence or absence of viewpoint effects depends upon the nature of the solids that are represented. Congenitally blind people do not spontaneously produce perspective drawings, but recent data suggests that depictions including linear perspective can be understood after minimal experience. The results suggest that two-dimensional configurations are not necessarily problematic for touch.

  5. The common operational picture as collective sensemaking

    NARCIS (Netherlands)

    Wolbers, J.J.; Boersma, F.K.

    2013-01-01

    The common operational picture is used to overcome coordination and information management problems during emergency response. Increasingly, this approach is incorporated in more advanced information systems. This is rooted in an 'information warehouse' perspective, which implies information can be

  6. The Heisenberg picture for single photon states

    International Nuclear Information System (INIS)

    Pienaar, Jacques; Myers, Casey; Ralph, Timothy C.

    2011-01-01

    In the context of quantum field theory, the Heisenberg picture has a distinct advantage over the Schrodinger picture because the Schrodinger picture requires us to transform the vacuum state itself, which can be intractable in the case of non-inertial reference frames, whereas the Heisenberg picture allows us to keep the same vacuum state and only transform the operators. However, the Heisenberg calculation requires the operators to already be expressed as a function of creation and annihilation operators acting on the original vacuum, whereas calculations in quantum information and quantum computation use operators that act on qubit states, necessarily containing particles. The relationship between the operators acting on these states and the operators acting on the vacuum state has remained elusive. We derive such an expression using an explicit model for single-particle production from the vacuum.

  7. Musicality in the Language of Picture Books

    Science.gov (United States)

    Heald, Robin

    2008-01-01

    The authors of picture books who write especially melodic language are doing more than simply offering up work that is pleasing to the ear. They are accessing more of the whole child. In this article five picture books will be discussed for their musical attributes: "Now One Foot, Now the Other", by Tomie dePaola, "The Cat in the Hat", by Dr.…

  8. Pictorial communication: Pictures and the synthetic universe

    Science.gov (United States)

    Ellis, Stephen R.

    1989-01-01

    Principles for the design of dynamic spatial instruments for communicating quantitative information to viewers are considered through a brief review of the history of pictorial communication. Pictorial communication is seen to have two directions: (1) from the picture to the viewer; and (2) from the viewer to the picture. Optimization of the design of interactive instruments using pictorial formats requires an understanding of the manipulative, perceptual, and cognitive limitations of human viewers.

  9. Examining lateralized semantic access using pictures.

    Science.gov (United States)

    Lovseth, Kyle; Atchley, Ruth Ann

    2010-03-01

    A divided visual field (DVF) experiment examined the semantic processing strategies employed by the cerebral hemispheres to determine if strategies observed with written word stimuli generalize to other media for communicating semantic information. We employed picture stimuli and vary the degree of semantic relatedness between the picture pairs. Participants made an on-line semantic relatedness judgment in response to sequentially presented pictures. We found that when pictures are presented to the right hemisphere responses are generally more accurate than the left hemisphere for semantic relatedness judgments for picture pairs. Furthermore, consistent with earlier DVF studies employing words, we conclude that the RH is better at accessing or maintaining access to information that has a weak or more remote semantic relationship. We also found evidence of faster access for pictures presented to the LH in the strongly-related condition. Overall, these results are consistent with earlier DVF word studies that argue that the cerebral hemispheres each play an important and separable role during semantic retrieval. Copyright 2009 Elsevier Inc. All rights reserved.

  10. TreePics: visualizing trees with pictures

    Directory of Open Access Journals (Sweden)

    Nicolas Puillandre

    2017-09-01

    Full Text Available While many programs are available to edit phylogenetic trees, associating pictures with branch tips in an efficient and automatic way is not an available option. Here, we present TreePics, a standalone software that uses a web browser to visualize phylogenetic trees in Newick format and that associates pictures (typically, pictures of the voucher specimens to the tip of each branch. Pictures are visualized as thumbnails and can be enlarged by a mouse rollover. Further, several pictures can be selected and displayed in a separate window for visual comparison. TreePics works either online or in a full standalone version, where it can display trees with several thousands of pictures (depending on the memory available. We argue that TreePics can be particularly useful in a preliminary stage of research, such as to quickly detect conflicts between a DNA-based phylogenetic tree and morphological variation, that may be due to contamination that needs to be removed prior to final analyses, or the presence of species complexes.

  11. The trace formula and the distribution of eigenvalues of Schroedinger operators on manifolds all of whose geodesics are closed

    International Nuclear Information System (INIS)

    Schubert, R.

    1995-05-01

    We investigate the behaviour of the remainder term R(E) in the Weyl formula {nvertical stroke E n ≤E}=Vol(M).E d/2 /[(4π) d/2 Γ(d/2+1)]+R(E) for the eigenvalues E n of a Schroedinger operator on a d-dimensional compact Riemannian manifold all of whose geodesics are closed. We show that R(E) is of the form E (d-1)/2 Θ(√E), where Θ(x) is an almost periodic function of Besicovitch class B 2 which has a limit distribution whose density is a box-shaped function. Furthermore we derive a trace formula and study higher order terms in the asymptotics of the coefficients related to the periodic orbits. The periodicity of the geodesic flow leads to a very simple structure of the trace formula which is the reason why the limit distribution can be computed explicitly. (orig.)

  12. Infinitely many conservation laws for two integrable lattice hierarchies associated with a new discrete Schroedinger spectral problem

    International Nuclear Information System (INIS)

    Zhu, Zuo-nong; Tam, Hon-Wah; Ding, Qing

    2003-01-01

    In this Letter, by means of considering matrix form of a new Schroedinger discrete spectral operator equation, and constructing opportune time evolution equations, and using discrete zero curvature representation, two discrete integrable lattice hierarchies proposed by Boiti et al. [J. Phys. A: Math. Gen. 36 (2003) 139] are re-derived. From the matrix Lax representations, we demonstrate the existence of infinitely many conservation laws for the two lattice hierarchies and give the corresponding conserved densities and the associated fluxes by means of formulae. Thus their integrability is further confirmed. Specially we obtain the infinitely many conservation laws for a new discrete version of the KdV equation. A connection between the conservation laws of the discrete KdV equation and the ones of the KdV equation is discussed by two examples

  13. Determination of the isotopic coefficient for x2N using a dimensional analysis of the Schroedinger equation

    International Nuclear Information System (INIS)

    Pali, R.; Coss, R. de; Mustre de Leon, J.

    1999-01-01

    The adimensionalization of equations which govern the dynamics of a physical system can be very useful when studying the qualitative behavior of any variable involved in those equations. In a dynamic system like a particle moving in an effective potential, the isotopic coefficient measure the degree of anharmonicity of the potential. In general each eigenstate has a different coefficient. In this work, we determined the isotopic coefficients for potentials of the form V(x) ∝ x 2N (N=1,2,3,...) through the adimensionalization process of the Schroedinger equation. We found an analytic expression for the isotopic coefficient which depends only of N but not on the eigenstate. The isotopic coefficient value starts at 1/2 for N=1 (harmonic potential) and gradually converges to 1.0 when N increments. This reflects the fact that the potential is more anharmonic for increasing N. (Author)

  14. Analytical solutions of the Schroedinger equation for a two-dimensional exciton in magnetic field of arbitrary strength

    Energy Technology Data Exchange (ETDEWEB)

    Hoang-Do, Ngoc-Tram; Hoang, Van-Hung; Le, Van-Hoang [Department of Physics, Ho Chi Minh City University of Pedagogy, 280 An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)

    2013-05-15

    The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schroedinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the energy of the ground and excited states are obtained with a very high precision of up to four decimal places. Especially, the precision is uniformly stable for the whole range of the magnetic field. This advantage appears due to the consideration of the asymptotic behaviour of the wave-functions in strong magnetic field. The results could be used for various physical analyses and the method used here could also be applied to other atomic systems.

  15. The discretized Schroedinger equation for the finite square well and its relationship to solid-state physics

    International Nuclear Information System (INIS)

    Boykin, Timothy B; Klimeck, Gerhard

    2005-01-01

    The discretized Schroedinger equation is most often used to solve one-dimensional quantum mechanics problems numerically. While it has been recognized for some time that this equation is equivalent to a simple tight-binding model and that the discretization imposes an underlying bandstructure unlike free-space quantum mechanics on the problem, the physical implications of this equivalence largely have been unappreciated and the pedagogical advantages accruing from presenting the problem as one of solid-state physics (and not numerics) remain generally unexplored. This is especially true for the analytically solvable discretized finite square well presented here. There are profound differences in the physics of this model and its continuous-space counterpart which are direct consequences of the imposed bandstructure. For example, in the discrete model the number of bound states plus transmission resonances equals the number of atoms in the quantum well

  16. Semantic interference from distractor pictures in single-picture naming: evidence for competitive lexical selection.

    Science.gov (United States)

    Jescheniak, Jörg D; Matushanskaya, Asya; Mädebach, Andreas; Müller, Matthias M

    2014-10-01

    Picture-naming studies have demonstrated interference from semantic-categorically related distractor words, but not from corresponding distractor pictures, and the lack of generality of the interference effect has been argued to challenge theories viewing lexical selection in speech production as a competitive process. Here, we demonstrate that semantic interference from context pictures does become visible, if sufficient attention is allocated to them. We combined picture naming with a spatial-cuing procedure. When participants' attention was shifted to the distractor, semantically related distractor pictures interfered with the response, as compared with unrelated distractor pictures. This finding supports models conceiving lexical retrieval as competitive (Levelt, Roelofs, & Meyer, 1999) but is difficult to reconcile with the response exclusion hypothesis (Finkbeiner & Caramazza, 2006b) proposed as an alternative.

  17. Single determinantal reaction theory as a Schroedinger analog: the time-dependent S-matrix Hartree-Fock method

    International Nuclear Information System (INIS)

    Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.; Kan, K.K.

    1979-01-01

    It is suggested that the TDHF method be viewed, not as an approximation to but as a model of the exact Schroedinger system; that is, as a gedanken many-body experiment whose analysis with digital computers provides data worthy in itself of theoretical study. From such a viewpoint attention is focused on the structural analogies of the TDHF system with the exact theory rather than upon its quantitative equivalence, and the TDHF many-body system is studied as a challenge of its own which, although much simpler than the realistic problem, may still offer complexity enough to educate theorists in the present state of knowledge. In this spirit, the TDHF description of continuum reactions can be restructured from an initial-value problem into a form analogous to the S-matrix version of the Schroedinger theory. The resulting TD-S-HF theory involves only self-consistent single determinantal solutions of the TDHF equations and invokes time averaging to obtain a consistent interpretation of the TDHF analogs of quantities which are constant in the exact theory, such as the S-matrix and the asymptotic reaction channel characteristics. Periodic solutions then play the role of stationary eigenstates in the construction of suitable asymptotic reaction channels. If these periodic channel states occur only at discrete energies, then the resulting channels are mutually orthogonal (on the time average) and the theory exhibits a structure fully analogous to the exact theory. In certain special cases where the periodic solutions are known to occur as an energy continuum, the requirement that the periodicity of the channel solutions be gauge invariant provides a natural requantization condition which (suggestively) turns out to be identical with the Bohr-Sommerfeld quantization rule. 11 references

  18. Picture Memory Improves with Longer On Time and Off Time

    Science.gov (United States)

    Tversky, Barbara; Sherman, Tracy

    1975-01-01

    Both recognition and recall of pictures improve as picture presentation time increases and as time between picture increases. This experiment was compared with an earlier one by Shaffer and Shiffrin (1972). (Editor/RK)

  19. Pictures with narration versus pictures with on-screen text during teaching Mathematics

    Directory of Open Access Journals (Sweden)

    Panagiotis Ioannou

    2017-06-01

    Full Text Available The purpose of the present study was to compare the effects of two different teaching methods on students’ comprehension in Mathematics: pictures with concurrent narration versus pictures with on-screen text, during teaching triangles, a lesson in Mathematics. Forty primary school children (boys and girls selected to participate in this study. Students splitted into two experimental groups with the technique of simple random sampling. The first group consisted of students who viewed and listened (pictures with narration group, while the second group consisted of students who viewed (pictures with on-screen text a presentation of triangles. A recall test was used to evaluate students’ comprehension. The results showed that students’ comprehension was better when triangles' presentation (pictures was accompanied with spoken words, than with printed words. The pictures with narration group performed better than the pictures with on-screen text group, in recall test (M = 4.97, SD = 1.32 p<0.01. Results are consistent with the modality principle in which learners are more likely to build connections between corresponding words and pictures when words are presented in a spoken form (narration simultaneously with pictures.

  20. Consideration of vision and picture quality: psychological effects induced by picture sharpness

    Science.gov (United States)

    Kusaka, Hideo

    1989-08-01

    A psychological hierarchy model of human vision(1)(2) suggests that the visual signals are processed in a serial manner from lower to higher stages: that is "sensation" - "perception" - "emotion." For designing a future television system, it is important to find out what kinds of physical factors affect the "emotion" experienced by an observer in front of the display. This paper describes the psychological effects induced by the sharpness of the picture. The subjective picture quality was evaluated for the same pictures with five different levels of sharpness. The experiment was performed on two kinds of printed pictures: (A) a woman's face, and (B) a town corner. From these experiments, it was found that the amount of high-frequency peaking (physical value of the sharpness) which psychologically gives the best picture quality, differs between pictures (A) and (B). That is, the optimum picture sharpness differs depending on the picture content. From these results, we have concluded that the psychophysical sharpness of the picture is not only determined at the stage of "perception" (e.g., resolution or signal to noise ratio, which everyone can judge immediately), but also at the stage of "emotion" (e.g., sensation of reality or beauty).

  1. The fast algorithm solving the one-dimensional time-dependent Schroedinger equation for teaching purposes

    International Nuclear Information System (INIS)

    Skoczen, A.; Machowski, W.; Kaprzyk, S.

    1990-07-01

    Computer program aiming at application in quantum mechanics didactics has been proposed. This program can generate the moving pictures of one-dimensional quantum mechanics scattering phenomena. Constructions of this program provide two options. In the first option the wave packet is generated in infinite one-dimensional well which has walls on the borders of graphic window. In the second option the square potential barrier is located in this well and transmission and reflection of wave packet are shown. We have selected a Gaussian wave packet to represent the initial state of the particle. The wave equation is solved numerically by a method discussed in detail. Solutions for the succesive time moments are graphically presented on the monitor screen. In this way observer can watch whole time-development of physical system. Graphically presented results are physically realistic when program parameters satisfy conditions discussed in this paper. (author)

  2. Sustained Attention Ability Affects Simple Picture Naming

    Directory of Open Access Journals (Sweden)

    Suzanne R. Jongman

    2017-07-01

    Full Text Available Sustained attention has previously been shown as a requirement for language production. However, this is mostly evident for difficult conditions, such as a dual-task situation. The current study provides corroborating evidence that this relationship holds even for simple picture naming. Sustained attention ability, indexed both by participants’ reaction times and individuals’ hit rate (the proportion of correctly detected targets on a digit discrimination task, correlated with picture naming latencies. Individuals with poor sustained attention were consistently slower and their RT distributions were more positively skewed when naming pictures compared to individuals with better sustained attention. Additionally, the need to sustain attention was manipulated by changing the speed of stimulus presentation. Research has suggested that fast event rates tax sustained attention resources to a larger degree than slow event rates. However, in this study the fast event rate did not result in increased difficulty, neither for the picture naming task nor for the sustained attention task. Instead, the results point to a speed-accuracy trade-off in the sustained attention task (lower accuracy but faster responses in the fast than in the slow event rate, and to a benefit for faster rates in the picture naming task (shorter naming latencies with no difference in accuracy. Performance on both tasks was largely comparable, supporting previous findings that sustained attention is called upon during language production.

  3. Different Loci of Semantic Interference in Picture Naming vs. Word-Picture Matching Tasks.

    Science.gov (United States)

    Harvey, Denise Y; Schnur, Tatiana T

    2016-01-01

    Naming pictures and matching words to pictures belonging to the same semantic category impairs performance relative to when stimuli come from different semantic categories (i.e., semantic interference). Despite similar semantic interference phenomena in both picture naming and word-picture matching tasks, the locus of interference has been attributed to different levels of the language system - lexical in naming and semantic in word-picture matching. Although both tasks involve access to shared semantic representations, the extent to which interference originates and/or has its locus at a shared level remains unclear, as these effects are often investigated in isolation. We manipulated semantic context in cyclical picture naming and word-picture matching tasks, and tested whether factors tapping semantic-level (generalization of interference to novel category items) and lexical-level processes (interactions with lexical frequency) affected the magnitude of interference, while also assessing whether interference occurs at a shared processing level(s) (transfer of interference across tasks). We found that semantic interference in naming was sensitive to both semantic- and lexical-level processes (i.e., larger interference for novel vs. old and low- vs. high-frequency stimuli), consistent with a semantically mediated lexical locus. Interference in word-picture matching exhibited stable interference for old and novel stimuli and did not interact with lexical frequency. Further, interference transferred from word-picture matching to naming. Together, these experiments provide evidence to suggest that semantic interference in both tasks originates at a shared processing stage (presumably at the semantic level), but that it exerts its effect at different loci when naming pictures vs. matching words to pictures.

  4. Emotionally negative pictures enhance gist memory.

    Science.gov (United States)

    Bookbinder, S H; Brainerd, C J

    2017-02-01

    In prior work on how true and false memory are influenced by emotion, valence and arousal have often been conflated. Thus, it is difficult to say which specific effects are caused by valence and which are caused by arousal. In the present research, we used a picture-memory paradigm that allowed emotional valence to be manipulated with arousal held constant. Negatively valenced pictures elevated both true and false memory, relative to positive and neutral pictures. Conjoint recognition modeling revealed that negative valence (a) reduced erroneous suppression of true memories and (b) increased the familiarity of the semantic content of both true and false memories. Overall, negative valence impaired the verbatim side of episodic memory but enhanced the gist side, and these effects persisted even after a week-long delay. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  5. Picture This: Young Quechua Children's Reactions to Imported Picture Books in Ayacucho, Peru

    Science.gov (United States)

    Eck, Jennifer Rowse

    2017-01-01

    Practitioners in ECE consider picture books an effective instructional tool in early childhood programming in the developed regions of the world. However, many young children from marginalized populations in the developing world have little to no access to them and thus, the effect that picture books could have upon their emergent literacy…

  6. Mariner Mars 1971 television picture catalog. Volume 2: Sequence design and picture coverage

    Science.gov (United States)

    Koskela, P. E.; Helton, M. R.; Seeley, L. N.; Zawacki, S. J.

    1972-01-01

    A collection of data relating to the Mariner 9 TV picture is presented. The data are arranged to offer speedy identification of what took place during entire science cycles, on individual revolutions, and during individual science links or sequences. Summary tables present the nominal design for each of the major picture-taking cycles, along with the sequences actually taken on each revolution. These tables permit identification at a glance, all TV sequences and the corresponding individual pictures for the first 262 revolutions (primary mission). A list of TV pictures, categorized according to their latitude and longitude, is also provided. Orthographic and/or mercator plots for all pictures, along with pertinent numerical data for their center points are presented. Other tables and plots of interest are also included. This document is based upon data contained in the Supplementary Experiment Data Record (SEDR) files as of 21 August 1972.

  7. Ubiquitous picture-rich content representation

    Science.gov (United States)

    Wang, Wiley; Dean, Jennifer; Muzzolini, Russ

    2010-02-01

    The amount of digital images taken by the average consumer is consistently increasing. People enjoy the convenience of storing and sharing their pictures through online (digital) and offline (traditional) media. A set of pictures can be uploaded to: online photo services, web blogs and social network websites. Alternatively, these images can be used to generate: prints, cards, photo books or other photo products. Through uploading and sharing, images are easily transferred from one format to another. And often, a different set of associated content (text, tags) is created across formats. For example, on his web blog, a user may journal his experiences of his recent travel; on his social network website, his friends tag and comment on the pictures; in his online photo album, some pictures are titled and keyword-tagged. When the user wants to tell a complete story, perhaps in a photo book, he must collect, across all formats: the pictures, writings and comments, etc. and organize them in a book format. The user has to arrange the content of his trip in each format. The arrangement, the associations between the images, tags, keywords and text, cannot be shared with other formats. In this paper, we propose a system that allows the content to be easily created and shared across various digital media formats. We define a uniformed data association structure to connect: images, documents, comments, tags, keywords and other data. This content structure allows the user to switch representation formats without reediting. The framework under each format can emphasize (display or hide) content elements based on preference. For example, a slide show view will emphasize the display of pictures with limited text; a blog view will display highlighted images and journal text; and the photo book will try to fit in all images and text content. In this paper, we will discuss the strategy to associate pictures with text content, so that it can naturally tell a story. We will also list

  8. Trace of nuclear energy with pictures

    International Nuclear Information System (INIS)

    1992-05-01

    This book traces the history of development over nuclear energy with pictures, which contains preface, development history of the world, development history of Korea, nuclear power plant in Kori, nuclear power plant in Wolseong, nuclear power plant in Yeonggwang, nuclear power plant in Uljin, nuclear fuel, using of radiation and radioactive isotope, development of nuclear energy in the world and a Chronological table of nuclear energy. This book is written to record the development history of Korea through pictures of the nuclear power plants in Korea.

  9. Automated Selection Of Pictures In Sequences

    Science.gov (United States)

    Rorvig, Mark E.; Shelton, Robert O.

    1995-01-01

    Method of automated selection of film or video motion-picture frames for storage or examination developed. Beneficial in situations in which quantity of visual information available exceeds amount stored or examined by humans in reasonable amount of time, and/or necessary to reduce large number of motion-picture frames to few conveying significantly different information in manner intermediate between movie and comic book or storyboard. For example, computerized vision system monitoring industrial process programmed to sound alarm when changes in scene exceed normal limits.

  10. [The changing picture of practicing dentistry].

    Science.gov (United States)

    Hokwerda, O

    2006-03-01

    Originally, dentists were particularly technical and curative practitioners. Nowadays, patient care is brought into focus, directed at maintaining oral health permanently by prevention and necessary curative treatments as a contribution to general health and well-being. The changing picture of praccising does not develop as a matter-of-course since many factors have an effect on dental practice. Effecting factors are: content concerning developments, technological advancements, legislation, government policies, organizational aspects, and typical characteristics of dental practitioners. The changing picture of practising dentistry is connected with uncertainty, proves to be hard to control, and some adjustments occur around practising.

  11. Gaze differences in processing pictures with emotional content.

    Science.gov (United States)

    Budimir, Sanja; Palmović, Marijan

    2011-01-01

    The International Affective Picture System (IAPS) is a set of standardized emotionally evocative color photographs developed by NIMH Center for Emotion and Attention at the University of Florida. It contains more than 900 emotional pictures indexed by emotional valence, arousal and dominance. However, when IAPS pictures were used in studying emotions with the event-related potentials, the results have shown a great deal of variation and inconsistency. In this research arousal and dominance of pictures were controlled while emotional valence was manipulated as 3 categories, pleasant, neutral and unpleasant pictures. Two experiments were conducted with an eye-tracker in order to determine to what the participants turn their gaze. Participants were 25 psychology students with normal vision. Every participant saw all pictures in color and same pictures in black/white version. This makes 200 analyzed units for color pictures and 200 for black and white pictures. Every picture was divided into figure and ground. Considering that perception can be influenced by color, edges, luminosity and contrast and since all those factors are collapsed on the pictures in IAPS, we compared color pictures with same black and white pictures. In first eye-tracking IAPS research we analyzed 12 emotional pictures and showed that participants have higher number of fixations for ground on neutral and unpleasant pictures and for figure on pleasant pictures. Second experiment was conducted with 4 sets of emotional complementary pictures (pleasant/unpleasant) which differ only on the content in the figure area and it was shown that participants were more focused on the figure area than on the ground area. Future ERP (event related potential) research with IAPS pictures should take into consideration these findings and to either choose pictures with blank ground or adjust pictures in the way that ground is blank. For the following experiments suggestion is to put emotional content in the figure

  12. Name agreement in picture naming : An ERP study

    NARCIS (Netherlands)

    Cheng, Xiaorong; Schafer, Graham; Akyürek, Elkan G.

    Name agreement is the extent to which different people agree on a name for a particular picture. Previous studies have found that it takes longer to name low name agreement pictures than high name agreement pictures. To examine the effect of name agreement in the online process of picture naming, we

  13. Some results of the spectra of random Schroedinger operators and their application to random point interaction models in one and three dimensions

    International Nuclear Information System (INIS)

    Kirsch, W.; Martinelli, F.

    1981-01-01

    After the derivation of weak conditions under which the potential for the Schroedinger operator is well defined the authers state an ergodicity assumption of this potential which ensures that the spectrum of this operator is a fixed non random set. Then random point interaction Hamiltonians are considered in this framework. Finally the authors consider a model where for sufficiently small fluctuations around the equilibrium positions a finite number of gaps appears. (HSI)

  14. Multisoliton solutions in terms of double Wronskian determinant for a generalized variable-coefficient nonlinear Schroedinger equation from plasma physics, arterial mechanics, fluid dynamics and optical communications

    International Nuclear Information System (INIS)

    Lue Xing; Zhu Hongwu; Yao Zhenzhi; Meng Xianghua; Zhang Cheng; Zhang Chunyi; Tian Bo

    2008-01-01

    In this paper, the multisoliton solutions in terms of double Wronskian determinant are presented for a generalized variable-coefficient nonlinear Schroedinger equation, which appears in space and laboratory plasmas, arterial mechanics, fluid dynamics, optical communications and so on. By means of the particularly nice properties of Wronskian determinant, the solutions are testified through direct substitution into the bilinear equations. Furthermore, it can be proved that the bilinear Baecklund transformation transforms between (N - 1)- and N-soliton solutions

  15. Neural Correlates of Processing Negative and Sexually Arousing Pictures

    Science.gov (United States)

    Bailey, Kira; West, Robert; Mullaney, Kellie M.

    2012-01-01

    Recent work has questioned whether the negativity bias is a distinct component of affective picture processing. The current study was designed to determine whether there are different neural correlates of processing positive and negative pictures using event-related brain potentials. The early posterior negativity and late positive potential were greatest in amplitude for erotic pictures. Partial Least Squares analysis revealed one latent variable that distinguished erotic pictures from neutral and positive pictures and another that differentiated negative pictures from neutral and positive pictures. The effects of orienting task on the neural correlates of processing negative and erotic pictures indicate that affective picture processing is sensitive to both stimulus-driven, and attentional or decision processes. The current data, together with other recent findings from our laboratory, lead to the suggestion that there are distinct neural correlates of processing negative and positive stimuli during affective picture processing. PMID:23029071

  16. Picture Communication in Papua New Guinea.

    Science.gov (United States)

    Cook, Bruce L.

    1980-01-01

    Reports the major findings of a study that investigated the effectiveness of using pictures of different art styles (stick figures, faceless outline drawings, detailed black-and-white, detailed black-and-white with watercolor wash, and black-and-white photographs) with 423 new readers in Papua New Guinea. (JD)

  17. Simple picture of the annihilation process

    International Nuclear Information System (INIS)

    Gotsman, E.; Nussinov, S.

    1980-01-01

    We propose a simple geometrical picture for B-barB annihilations, which is motivated by the electric-flux-tube model and is consistent with the quark-rearrangement model, as well as the nonplanar multiperipheral quark-exchange model. Within its framework we are able to explain all the salient features of the experimental annihilation data

  18. Development of a Rich Picture editor

    DEFF Research Database (Denmark)

    Valente, Andrea; Marchetti, Emanuela

    2010-01-01

    rich picture practice into software proved difficult, therefore, we decided to follow a user-centered approach: design and implement a prototype with basic functionalities, then run a usability test with a few students and professionals. The feedback collected in the test validated our hypothesis circa...

  19. A picture dictionary of electric glossary

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1974-01-15

    This book has a lot of explanations on electric glossary with picture, which include basic important glossaries like nuclear, current theory, measuring, electro genesis, power transmission, supply of electric power, a rotary machine, application of electromotive force, electronic engineering, automatic control, electronic calculator, T.V and communication, material of electricity, electrochemistry, traffic, electric work, lighting and electric heater, regulations and standard.

  20. Behavioral modulation by mutilation pictures in women

    Directory of Open Access Journals (Sweden)

    Pereira M.G.

    2004-01-01

    Full Text Available Previous studies have shown that women are more emotionally expressive than men. It is unclear, however, if women are also more susceptible to the emotional modulation of behavior imposed by an affective stimulus. To investigate this issue, we devised a task in which female subjects performed six sequential trials of visual target detection following the presentation of emotional (mutilation and erotic or neutral pictures (domestic utensils and objects and compared the data obtained in the present study with those described in a previous study with male subjects. The experiment consisted of three blocks of 24 pictures and each block had an approximate duration of 4 min. Our sample consisted of 36 subjects (age range: 18 to 26 years and each subject performed all blocks. Trials following the presentation of mutilation pictures (283 ms had significantly slower reaction times than those following neutral (270 ms pictures. None of the trials in the "pleasant block" (271 ms was significantly different from those in the "neutral block". The increase in reaction time observed in the unpleasant block may be related in part to the activation of motivational systems leading to an avoidance behavior. The interference effect observed in this study was similar to the pattern previously described for men. Thus, although women may be more emotionally expressive, they were not more reactive to aversive stimuli than men, as measured by emotional interference in a simple reaction time task.

  1. Occlusion classifiers for picture rate conversion

    NARCIS (Netherlands)

    Bartels, C.L.L.; Haan, de G.; Rabbani, Majid

    2009-01-01

    Occlusion detection is an essential ingredient in high quality picture rate up-conversion and view interpolation applications. Many integrated approaches to occlusion detection and classification have been proposed, particularly in the stereo literature. However, due to their high complexity and

  2. The Oxford Picture Dictionary. Beginning Workbook.

    Science.gov (United States)

    Fuchs, Marjorie

    The beginning workbook of the Oxford Picture Dictionary is in full color and offers vocabulary reinforcement activities that correspond page for page with the dictionary. Clear and simple instructions with examples make it suitable for independent use in the classroom or at home. The workbook has up-to-date art and graphics, explaining over 3700…

  3. Thermodynamic picture of the glassy state

    NARCIS (Netherlands)

    Nieuwenhuizen, T.M.

    2000-01-01

    A picture for the thermodynamics of the glassy state is introduced. It assumes that one extra parameter, the effective temperature, is needed to describe the glassy state. This explains the classical paradoxes concerning the Ehrenfest relations and the Prigogine-Defay ratio. As a second feature, the

  4. A Bridge between Pictures and Print.

    Science.gov (United States)

    Jeffree, Dorothy

    1981-01-01

    The experiment investigated the feasibility of bridging the gap between the recognition of pictures and the recognition of words in four mentally handicapped adolescents by adapting a modified version of symbol accentuation (in which a printed word looks like the object it represents). (SB)

  5. Aesthetics and Children's Picture-Books

    Science.gov (United States)

    Leddy, Thomas

    2002-01-01

    Some writers on children's picture-books seem to believe that comfort and reassurance are their most important goals. Yet these books may also provide a context for imaginative adventure, and even for a journey into the dark night of the soul. As Nietzsche would put it, there is a Dionysian as well as an Apollonian element in children's…

  6. Picture Books Stimulate the Learning of Mathematics

    Science.gov (United States)

    van den Heuvel-Panhuizen, Marja; van den Boogaard, Sylvia; Doig, Brian

    2009-01-01

    In this article we describe our experiences using picture books to provide young children (five- to six-year-olds) with a learning environment where they can explore and extend preliminary notions of mathematics-related concepts, without being taught these concepts explicitly. We gained these experiences in the PICO-ma project, which aimed to…

  7. Constructing Meaning in Interaction through Picture Books

    Science.gov (United States)

    Lugossy, Réka

    2012-01-01

    This qualitative study describes and analyses young language learners' spontaneous comments while sharing picture books during EFL sessions. It also explores teachers' responses to learners' comments, and considers reasons teachers may choose to ignore children's talk in their first language (L1). Data were collected from young Hungarian learners…

  8. A picture dictionary of electric glossary

    International Nuclear Information System (INIS)

    1974-01-01

    This book has a lot of explanations on electric glossary with picture, which include basic important glossaries like nuclear, current theory, measuring, electro genesis, power transmission, supply of electric power, a rotary machine, application of electromotive force, electronic engineering, automatic control, electronic calculator, T.V and communication, material of electricity, electrochemistry, traffic, electric work, lighting and electric heater, regulations and standard.

  9. Picture Book Soldiers: Men and Messages.

    Science.gov (United States)

    Desai, Christina M.

    2001-01-01

    Examines children's picture books about soldiers and war, including fiction, folktales, and historical fiction, analyzing their implicit and explicit messages about war and the military, and evaluating them for gender stereotyping. Finds that the soldiers conform almost uniformly to an exaggerated male stereotype. Shows different value judgments…

  10. The changing picture of practicing dentistry

    NARCIS (Netherlands)

    Hokwerda, O

    2006-01-01

    Originally, dentists were particularly technical and curative practitioners. Nowadays, patient care is brought into focus, directed at maintaining oral health permanently by prevention and necessary curative treatments as a contribution to general health and well-being. The changing picture of

  11. My America in Poetry and Pictures.

    Science.gov (United States)

    Pappas, Marjorie L.

    2003-01-01

    Describes a unit that provides opportunities for students to examine the relationship between poetry and pictures as they select published poems, write their own poetry, and take photographs to accompany the poems in an anthology. Describes lesson one on intellectual property and copyright, and lesson two on appreciation. Includes a unit guide and…

  12. Princess Picture Books: Content and Messages

    Science.gov (United States)

    Dale, Lourdes P.; Higgins, Brittany E.; Pinkerton, Nick; Couto, Michelle; Mansolillo, Victoria; Weisinger, Nica; Flores, Marci

    2016-01-01

    Because many girls develop their understanding of what it means to be a girl from books about princesses, the researchers coded the messages and content in 58 princess books (picture, fairy tales, and fractured fairy tales). Results indicate that gender stereotypes are present in the books--the princesses were more likely to be nurturing, in…

  13. Semantic category interference in overt picture naming

    NARCIS (Netherlands)

    Maess, B.; Friederici, A.D.; Damian, M.F.; Meyer, A.S.; Levelt, W.J.M.

    2002-01-01

    The study investigated the neuronal basis of the retrieval of words from the mental lexicon. The semantic category interference effect was used to locate lexical retrieval processes in time and space. This effect reflects the finding that, for overt naming, volunteers are slower when naming pictures

  14. The Last Great American Picture Show

    NARCIS (Netherlands)

    Elsaesser, Thomas; King, Noel; Horwath, Alexander

    2004-01-01

    The Last Great American Picture Show brings together essays by scholars and writers who chart the changing evaluations of the American cinema of the 1970s, sometimes referred to as the decade of the lost generation, but now more and more recognized as the first New Hollywood, without which the

  15. 32 CFR 705.8 - Motion pictures.

    Science.gov (United States)

    2010-07-01

    ... OFFICIAL RECORDS PUBLIC AFFAIRS REGULATIONS § 705.8 Motion pictures. (a) The rules and procedures given in... Defense (Public Affairs) for clearance for public release. They will be accompained by five copies of the... Assistant Secretary of Defense (Public Affairs). [41 FR 29101, July 15, 1976, as amended at 44 FR 6390, Feb...

  16. Positive erotic picture stimuli for emotion research in heterosexual females.

    Science.gov (United States)

    Jacob, Gitta Anne; Arntz, Arnoud; Domes, Gregor; Reiss, Neele; Siep, Nicolette

    2011-12-30

    In most experimental studies, emotional pictures are widely used as stimulus material. However, there is still a lack of standardization of picture stimuli displaying erotic relationships, despite the association between a number of psychological problems and severe impairments and problems in intimate relationships. The aim of the study was to test a set of erotic stimuli, with the potential to be used in experimental studies, with heterosexual female subjects. Twenty International Affective Picture System (IAPS) pictures and an additional 100 pictures showing romantic but not explicitly sexual scenes and/or attractive single males were selected. All pictures were rated with respect to valence, arousal, and dominance by 41 heterosexual women and compared to pictures with negative, positive, and neutral emotional valence. Erotic IAPS pictures and our additional erotic pictures did not differ in any of the evaluation dimensions. Analyses of variance (ANOVAs) for valence, arousal, and dominance comparing different picture valence categories showed strong effects for category. However, valence was not significantly different between erotic and positive pictures, while arousal and control were not significantly different between positive and neutral pictures. The pictures of our new set are as positive for heterosexual women as highly positive IAPS pictures, but higher in arousal and dominance. The picture set can be used in experimental psychiatric studies requiring high numbers of stimuli per category. Limitations are the restriction of stimuli application to heterosexual females only and to self-report data. Copyright © 2011 Elsevier Ltd. All rights reserved.

  17. Revisiting the picture-superiority effect in symbolic comparisons: do pictures provide privileged access?

    Science.gov (United States)

    Amrhein, Paul C; McDaniel, Mark A; Waddill, Paula

    2002-09-01

    In 4 experiments, symbolic comparisons were investigated to test semantic-memory retrieval accounts espousing processing advantages for picture over word stimuli. In Experiment 1, participants judged pairs of animal names or pictures by responding to questions probing concrete or abstract attributes (texture or size, ferocity or intelligence). Per pair, attributes were salient or nonsalient concerning their prerated relevance to animals being compared. Distance (near or far) between attribute magnitudes was also varied. Pictures did not significantly speed responding relative to words across all other variables. Advantages were found forfar attribute magnitudes (i.e., the distance effect) and salient attributes. The distance effect was much less for salient than nonsalient concrete-attribute comparisons. These results were consistently found in additional experiments with increased statistical power to detect modality effects. Our findings argue against dual-coding and some common-code accounts of conceptual attribute processing, urging reexamination of the assumption that pictures confer privileged access to long-term knowledge.

  18. Get the picture? The effects of iconicity on toddlers' reenactment from picture books.

    Science.gov (United States)

    Simcock, Gabrielle; DeLoache, Judy

    2006-11-01

    What do toddlers learn from everyday picture-book reading interactions? To date, there has been scant research exploring this question. In this study, the authors adapted a standard imitation procedure to examine 18- to 30-month-olds' ability to learn how to reenact a novel action sequence from a picture book. The results provide evidence that toddlers can imitate specific target actions on novel real-world objects on the basis of a picture-book interaction. Children's imitative performance after the reading interaction varied both as a function of age and the level of iconicity of the pictures in the book. These findings are discussed in terms of children's emerging symbolic capacity and the flexibility of the cognitive representation.

  19. Digital Picture Production and Picture aesthetic Competency in It-didactic Design

    DEFF Research Database (Denmark)

    Rasmussen, Helle

    , that It and media are only used seldom by 21 % of teachers in Visual Arts and 7 % of teachers in this subject never use It and Media in these lessons. Art teachers – among others - also express the need for continuing education. (Ministeriet for Børn og Undervisning 2011). Since lessons in digital picture...... production have been a demand in Visual Arts in Danish schools for more than two decades, these conditions call for development of new didactic knowledge. Besides new genres and ways of using digital pictures and media continuously develop. (Sørensen 2002). This ought to be an incessant challenge...... subject Visual Arts – and crosswise of subjects in school. The overall research question has been: How can IT-didactic designs support lessons in production of complex meaning in digital pictures and increase the development of pupil’s picture aesthetic competences? By using the expression ‘complex...

  20. A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Nash, Patrick L.

    2008-01-01

    Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation Δ perpendicular FDA of 1/r (∂)/(∂r) r(∂)/(∂r) that possesses an associated exact unitary representation of e i/2λΔ perpendicular FDA . The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown to be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium

  1. The inverse problem for the one-dimensional Schroedinger equation with an energy-dependent potential. II

    International Nuclear Information System (INIS)

    Jaulent, M.; Jean, C.

    1976-01-01

    The one-dimensional Schroedinger equation y + ''+ ) 7k 2 -V + (k,x){y + =0, x belonging to R, was previously considered when the potential V + (k,x) depends on the energy k 2 in the following way: V + (k,x)=U(x)+2kQ(x), (U(x), Q(x)) belonging to a large class of pairs of real potentials admitting no bound state). The two systems of differential and integral equations then introduced are solved. Then, investigating the inverse scattering problem it is found that a necessary and sufficient condition for one of the functions S + (k) and Ssub(-1)sup(+)(k) to be the scattering matrix associated with a pair (U(x), Q(x)) is that S + (k) (or equivalently Ssub(-1)sup(+)(k) belongs to the class S introduced. This pair is the only one admitting this function as its scattering matrix. Investigating the inverse reflection problem, it is found that a necessary and sufficient condition for a function S 21 + (k) to be the reflection coefficient to the right associated with a pair (U(x), Q(x)) is that S 21 + (k) belongs to the class R introduced. This pair is the only one admitting this function as

  2. Continuity and completeness in physical theory: Schroedinger's return to the wave interpretation of quantum mechanics in the 1950's

    International Nuclear Information System (INIS)

    D'Agostino, S.

    1992-01-01

    In the 50s, Schroedinger proposed a new conception of a continuous theory of Quantum Mechanics, which remarkably modified his 1926 ideas on ondulatory mechanics. The lack of individuality of the atomic particles presented in the new statistics, and in Heisenberg's Indeterminacy Relations, was by him considered as an aspect of a more general crisis in the anthology itself of classical atomism. Unlike his 1926 ideas, he proposed now to represent the wave equation in an n-dimensional space and he considered second-quantization technique as the proper mathematical tool for his new physical conception. Although he accepted that space-time discontinuities and casual gaps may appear here and there on the observational level (e.g. in the Indeterminacy Relations), he was convinced that they could be made compatible with a continuous pure theory, provided one accepted a suitable conception of the theory's epistemiological status. For him, only a continuous theory satisfied the conditions for a complete theory. On these matters, he thought he was somehow orthodox to the ideas of Hertz and Boltzmann, which were also reflected in the teaching of Exner. (author). 69 refs

  3. Penggunaan Model Pembelajaran Picture and Picture Untuk Meningkatkan Kemampuan Siswa Menulis Karangan

    Directory of Open Access Journals (Sweden)

    Heriyanto Heriyanto

    2014-02-01

    Full Text Available Menulis merupakan keterampilan berbahasa yang kompleks, produktif dan ekspresif, karena penulis harus terampil menggunakan grofologi, struktur bahasa dan memiliki pengetahuan bahasa yang memadai, untuk itu perlu dilatih secara teratur dan cermat sejak kelas awal SD. Karangan sebagai salah satu hasil karya menulis, merupakan hasil pekerjaan dari mengarang. Menulis karangan dalam penelitian ini adalah menulis karangan narasi. Salah satu masalah dalam pembelajaran Bahasa Indonesia adalah kesulitan siswa dalam menulis karangan yang baik dan benar, yang juga terjadi pada siswa kelas IVA SDN Pinggir Papas 1. Pembelajaran menulis karangan dengan menggunakan model kooperatif tipe picture and picture  diharapkan mampu meningkatkan pemahaman siswa dalam hal menulis karangan. Untuk itu, dilakukan penelitian terhadap siswa kelas IVA SDN Pinggir Papas I Kecamatan Kalianget Kabupaten Sumenep yang berjumlah 33 siswa. Penelitian dengan judul “Penggunaan Model Pembelajaran Kooperatif Tipe Picture and Picture untuk Meningkatkan Kemampuan Siswa Menulis Karangan” ini menggunakan penelitian tindakan kelas sebanyak dua putaran. Setiap putaran terdiri dari tahap rancangan, kegiatan, pengamatan, dan refleksi. Data yang diperoleh berupa nilai hasil LKS dan kuis individu berupa menulis karangan, lembar observasi aktivitas guru dan siswa serta penilaian penggunaan model pembelajaran kooperatif picture and picture, juga hasil respon siswa. Dari hasil analis menunjukkan bahwa penggunaan model pembelajaran kooperatif tipe picture and picture dapat meningkatkan kemampuan menulis karangan siswa kelas IVA SDN Pinggir Papas 1. Peningkatan ini terjadi pada nilai rata-rata LKS, yaitu dari 55 menjadi 71,6. Adapun hasil karangan individu siswa dari rata-rata 56,7 dengan ketuntasan 55% menjadi 74,5 dengan ketuntasan mencapai 88% atau terjadi peningkatan sebesar 33% dari siklus I.

  4. Dwarfism and gigantism in historical picture postcards.

    OpenAIRE

    Enderle, A

    1998-01-01

    A collection of 893 historical picture postcards from 1900 to 1935, depicting dwarfs and giants, was analysed from medical and psychosocial viewpoints. In conditions such as 'bird headed dwarfism', achondroplasia, cretinism, so-called Aztecs or pinheads, Grebe chondrodysplasia, and acromegalic gigantism, the disorder could be diagnosed easily. In hypopituitary dwarfism, exact diagnosis was more difficult because of heterogeneity. The most common conditions depicted were pituitary dwarfism and...

  5. Enhancement of blurred pictures by spatial filtering

    International Nuclear Information System (INIS)

    Wolton, W.P.; Redman, J.D.

    Substantial improvement in the intelligibility of defocussed pictures has been demonstrated using coherent optical processing. Correction for penumbra effects, such as arise in radiography, has been demonstrated at optical wavelengths. Compensation for a Gaussian spread function, such as might occur in radiography via a salt screen, has also been demonstrated. A simulation has shown that much greater enhancement could be expected if improved phase filters could be made

  6. Superconformal ghost correlators and picture changing

    International Nuclear Information System (INIS)

    Bonini, M.; Iengo, R.; Nunez, C.

    1988-12-01

    We compute the correlation functions for the system of superconformal ghosts β, γ(λ=3/2), including the corresponding spin fields, on arbitrary Riemann surfaces. Using fermionization, defined as a change of variables in the functional integration, we derive and generalize previous results obtained by bosonization. As an application we study the picture changing mechanism in the Ramond sector of the superstring. (author). 11 refs

  7. Cut and paste pictures in surrealism

    Directory of Open Access Journals (Sweden)

    Todić Milanka

    2006-01-01

    Full Text Available Proceeding from the idea of the readymade, Marko Ristić’s, Vane Bor’s and Dušan Matić’s collages regroup readymade pictorial and textual matrices according to the rules of free associative syntax. Everything that they collected cut out and pasted bears the hallmark of personal choice, i.e. objective chance, as the Surrealists would say. In the new structure of the collage, picture and text were of equal importance. However, we should not forget that both picture and text were only fragments, of different origin so that they could not function as autonomous elements in their own right nor could they establish logical interlinks. Cut and paste picture in Surrealism are primarily registered as visual wholes, in which the former principle of harmony has been substituted by the principle of discontinuity. In fact, they do not aspire to establish closed and unambiguous semantic structures either on a single paper or within a cycle, disregarding as they do conventional narrative and illustrative order in representing reality.

  8. Analysis of book colections Great picture book for preschoolers

    OpenAIRE

    Cunk, Tina

    2013-01-01

    Thesis entitled ˝Analysis of book collections Great picture book for preschoolers˝ is based on theoretical approach and empirical study. In the theoretical part I focused on the development of youth literature and the definition of the latter, furthermore I described Great picture book and definition of picture book, I presented four versions of picture books in the Slovenian area, described types of picture books and wrote translation of Maria Nikolaeva´s picture book and her point of view...

  9. Where and how morphologically complex words interplay with naming pictures.

    Science.gov (United States)

    Zwitserlood, Pienie; Bölte, Jens; Dohmes, Petra

    2002-01-01

    Two picture-word experiments are reported in which a delay of 7 to 10 was introduced between distractor and picture. Distractor words were either derived words (Experiment 1) or compounds (Experiment 2), morphologically related to the picture name. In both experiments, the position of morphological overlap between distractor (e.g., rosebud vs tea-rose) and picture name (rose) was manipulated. Clear facilitation of picture naming latencies was obtained when pictures were paired with morphological distractors, and effects were independent of distractor type and position of overlap. The results are evaluated against "full listing" and "decomposition" approaches of morphological representation. Copyright 2002 Elsevier Science (USA).

  10. Deprivation selectively modulates brain potentials to food pictures

    OpenAIRE

    Stockburger, Jessica; Weike, Almut I.; Hamm, Alfons O.; Schupp, Harald Thomas

    2008-01-01

    Event-related brain potentials (ERPs) were used to examine whether the processing of food pictures is selectively modulated by changes in the motivational state of the observer. Sixteen healthy male volunteers were tested twice 1 week apart, either after 24 hr of food deprivation or after normal food intake. ERPs were measured while participants viewed appetitive food pictures as well as standard emotional and neutral control pictures. Results show that the ERPs to food pictures in a hungry, ...

  11. Physical interpretation of Monte Carlo wave-function and stochastic Schroedinger equation methods for cavity quantum electrodynamics

    International Nuclear Information System (INIS)

    Kist, Tarso B.L.; Orszag, M.; Davidovich, L.

    1997-01-01

    The dynamics of open system is frequently modeled in terms of a small system S coupled to a reservoir R, the last having an infinitely larger number of degree of freedom than S. Usually the dynamics of the S variables may be of interest, which can be studied using either Langevin equations, or master equations, or yet the path integral formulation. Useful alternatives for the master equation method are the Monte Carlo Wave-function method (MCWF), and Stochastic Schroedinger Equations (SSE's). The methods MCWF and SSE's recently experienced a fast development both in their theoretical background and applications to the study of the dissipative quantum systems dynamics in quantum optics. Even though these alternatives can be shown to be formally equivalent to the master equation approach, they are often regarded as mathematical tricks, with no relation to a concrete physical evolution of the system. The advantage of using them is that one has to deal with state vectors, instead of density matrices, thus reducing the total amount of matrix elements to be calculated. In this work, we consider the possibility of giving a physical interpretation to these methods, in terms of continuous measurements made on the evolving system. We show that physical realizations of the two methods are indeed possible, for a mode of the electromagnetic field in a cavity interacting with a continuum of modes corresponding to the field outside the cavity. Two schemes are proposed, consisting of a mode of the electromagnetic field interacting with a beam of Rydberg two-level atoms. In these schemes, the field mode plays the role of a small system and the atomic beam plays the role of a reservoir (infinitely larger number of degrees of freedom at finite temperature, the interaction between them being given by the Jaynes-Cummings model

  12. Memory for Pictorial Information and the Picture Superiority Effect.

    Science.gov (United States)

    Maisto, Albert A.; Queen, Debbie Elaine

    1992-01-01

    The performance of 53 younger adults (mean age 20.7) and 52 older adults (mean age 68.3) was compared in a memory task involving pictures, words, and pictures-plus-words. Results showed (1) significantly higher recall scores for younger adults; (2) equivalent picture superiority effect for both groups; and (3) decline in older adults' performance…

  13. Picture This: 4-H Press Corps Builds Life Skills

    Science.gov (United States)

    Clary, Christy D.

    2018-01-01

    A picture is worth a thousand words! Extension professionals are often looking for the picture that best captures an event and tells its story. Look beneath the surface, though, and a picture is worth much more. Developing a 4-H press corps results in a collection of useful photos but has the added benefit of providing 4-H members with an…

  14. Promoting Self-Questioning through Picture Book Illustrations

    Science.gov (United States)

    Lohfink, Gayla

    2013-01-01

    This teaching tip manuscript demonstrates how picture book illustrations can be used as an inquiry tool that facilitates one's connecting of visual investigations in a picture to the process of generating self-questions. Techniques suggested to promote self-questioning are (1) introducing young readers to an interactive picture book read aloud…

  15. The Development of the Picture-Superiority Effect

    Science.gov (United States)

    Whitehouse, Andrew J. O.; Maybery, Murray T.; Durkin, Kevin

    2006-01-01

    When pictures and words are presented serially in an explicit memory task, recall of the pictures is superior. While this effect is well established in the adult population, little is known of the development of this picture-superiority effect in typical development. This task was administered to 80 participants from middle childhood to…

  16. The Progress of Students Reading Comprehension through Wordless Picture Books

    Science.gov (United States)

    Lubis, Romaida

    2018-01-01

    Wordless picture book is an unique book that could help the young learner to get their literacy. The content of the wordless picture book must be communicated through the visual of the illustration. This research discusses a case study of how a kid of six years old produce his narrative through wordless picture book. The kid was allowed to see and…

  17. Emotionally arousing pictures increase blood glucose levels and enhance recall.

    Science.gov (United States)

    Blake, T M; Varnhagen, C K; Parent, M B

    2001-05-01

    Arousal enhances memory in human participants and this enhancing effect is likely due to the release of peripheral epinephrine. As epinephrine does not readily enter the brain, one way that peripheral epinephrine may enhance memory is by increasing circulating blood glucose levels. The present study investigated the possibility that emotionally arousing color pictures would improve memory and elevate blood glucose levels in human participants. Blood glucose levels were measured before, 15 min, and 30 min after male university students viewed 60 emotionally arousing or relatively neutral pictures. Participants viewed each picture for 6 s and then had 10 s to rate the arousal (emotional intensity) and valence (pleasantness) of each picture. A free-recall memory test was given 30 min after the last picture was viewed. Although the emotionally arousing and neutral picture sets were given comparable valence ratings, participants who viewed the emotionally arousing pictures rated the pictures as being more arousing, recalled more pictures, and had higher blood glucose levels after viewing the pictures than did participants who viewed the neutral pictures. These findings indicate that emotionally arousing pictures increase blood glucose levels and enhance memory, and that this effect is not due to differences in the degree of pleasantness of the stimuli. These findings support the possibility that increases in circulating blood glucose levels in response to emotional arousal may be part of the biological mechanism that allows emotional arousal to enhance memory. Copyright 2001 Academic Press.

  18. Design Considerations for Multi-Channel Picture Communication Networks

    OpenAIRE

    Scheibe, Paul O.

    1983-01-01

    Design of networks intended for communication of digitally-encoded pictures involves considerations different from those used in the design of text or voice communication networks. This paper provides an overview of the elements useful in the design of picture communication networks by relation and contrast with other communication networks. Particular emphasis is given to picture communication systems useful in medical applications.

  19. Picture archiving and communications systems (PACS)

    International Nuclear Information System (INIS)

    Huang, H.K.; Dwyer, S.J. III; Angus, W.M.; Capp, M.P.; Arenson, R.L.; Kangarloo, H.

    1987-01-01

    This special focus session discusses the current status of picture archiving and communication systems (PACS). The first presentation focuses on the technological advances in various PACS components. The second presentation concentrates on image archiving - what is required, what is available. The third talk is on the concept of a total digital radiology department in the past, the present, and the future. The fourth panelist discusses evaluating various imaging systems as PACS components for the intensive care unit. Finally, one hears about clinical experience with two operating PACS modules, one in pediatric radiology and the second in a coronary care unit

  20. Picturing diversity in the ATLAS experiment.

    CERN Document Server

    Biondi, Silvia; The ATLAS collaboration

    2017-01-01

    With over 3,000 members from 178 institutes, the ATLAS Collaboration is naturally diverse. However, capturing this diversity through pictures can be a challenge. Photography is a powerful tool, allowing us to reveal the faces behind a story and give the public the unique opportunity to understand and appreciate the human aspects of ATLAS’s scientific research. The role of photographs in portraying the diversity of the ATLAS Collaboration will be described. Their role on various communication platforms will be described and their impact examined, with focus on engagement of new audiences.