2d quantum-mechanical problem of the time evolution of a particle in a quadratic potential is studied. We suppose that the center of the potential is displaced in arbitrary way in time. An analytical expression for the wave function in arbitrary instant time was built. It is shown the dynamic shift of the center of the potential doesn’t change the variance. Moreover, the system can exhibit the resonance: when the frequency of the potential perturbation approaches to the natural frequency the amplitude of the wave packet of particle is increased.2d quantum-mechanical problem of the time evolution of a particle in a quadratic potential is studied. We suppose that the center of the potential is displaced in arbitrary way in time. An analytical expression for the wave function in arbitrary instant time was built. It is shown the dynamic shift of the center of the potential doesn’t change the variance. Moreover, the system can exhibit the resonance: when the frequency of the potential perturbation approaches to the natural frequency the amplitude of the wave packet of particle is increased.

Journal of Nano- and Electronic PhysicsJan 1, 20162 citations

New approach to perturbation theory of many-particle systems

Colin John Lambert, W. E. Hagston

International Journal of Theoretical PhysicsFeb 1, 19840 citations

Analytic, group-theoretic density profiles for confined, correlated N -body systems

W. Blake Laing, Martin Dunn, D. K. Watson

Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed-matter, atomic, and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed-matter, atomic, and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.

arXiv:cond-mat/0607600Physical Review ADec 5, 200613 citations

Perturbation theory of large quantum systems

Nicolaas Marinus Hugenholtz

PhysicaJan 1, 1957463 citations

The Quantum Mechanics of N-Particle Systems

Pure and applied physicsJan 1, 19700 citations

Analytic perturbation theory and localization phenomena

Erkki Brändas, C. H. Obcemea

Abstract This paper attempts to apply the results of analytic perturbation theory to systems exhibiting some degree of randomness in their state variables. In particular, we focus on the localization problem in the Anderson model. It is shown that this approach proves the existence of bound states as a result of the statistical treatment of the Weinberg–van Winter–Hunziker irreducible N‐particle kernel. The analysis is extended beyond the one‐particle cluster approach and the occurrence of higher‐order clusters is discussed in relation to the diluteness criterion and the conditions set on the interaction potential V.Abstract This paper attempts to apply the results of analytic perturbation theory to systems exhibiting some degree of randomness in their state variables. In particular, we focus on the localization problem in the Anderson model. It is shown that this approach proves the existence of bound states as a result of the statistical treatment of the Weinberg–van Winter–Hunziker irreducible N‐particle kernel. The analysis is extended beyond the one‐particle cluster approach and the occurrence of higher‐order clusters is discussed in relation to the diluteness criterion and the conditions set on the interaction potential V.

International Journal of Quantum ChemistryNov 1, 19790 citations

Confined quantum systems involving

N

identical interacting particles are to be found in many areas of physics, including condensed-matter, atomic, and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.