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Quasiclassical trajectory coherent states of nonrelativistic particle in a homogeneous magnetic field. Kvaziklassicheskie traektorno-kogerentnye sostoyaniya nerelyativistskoj chastitsy v odnorodnom magnitnom pole

Belov, D Boltovskij, A. G. Karavaev

Published Jun 1, 1990• 0 citations
OpenAlex

Abstract

Nonrelativistic particle in a homogeneous magnetic field was taken as an example to illustrate the general structure of quasiclassical trajectory - coherent states. Relation of these states (representing exact solutions in the case of quadratic nonrelativistic quantum systems) with widely known coherent and correlated coherent states was established.

Related papers

Quasiclassical trajectory-coherent states of a spinless relativistic particle in a constant homogeneous magnetic field. Kvaziklassicheskie traektorno-kogerentnye sostoyaniya besspinovoj relyativistskoj chastitsy v postoyannom odnorodnom magnitnom pole

D Boltovskij, A. G. Karavaev

•May 1, 1989•0 citations

Quasiclassical trajectory-coherent states of a particle in an arbitrary electromagnetic field

Vladislav G. Bagrov, Владимир Владимирович Белов, I. M. Ternov

In this paper we show that for a nonrelativistic charged particle moving in an arbitrary external electromagnetic field there exist approximate solutions of the Schrödinger equation, such that the quantum-mechanical averages of the coordinates and the momenta with respect to these states are general exact solutions of the classical Hamiltonian equations. Such states are called trajectory-coherent states. The wave functions of the trajectory-coherent states are obtained by the complex germ method by V. P. Maslov. The simplest properties of these states are studied.

Journal of Mathematical Physics•Dec 1, 1983•48 citations

Quasiclassical trajectory-coherent states of a nonrelativistic particle in an arbitrary electromagnetic field

Vladislav G. Bagrov, Владимир Владимирович Белов, I. M. Ternov

Theoretical and Mathematical Physics•Mar 1, 1982•47 citations

Generalized coherent states for electrons in external fields and application to potential scattering

Sándor Varró, F. Ehlotzky

By continuing earlier investigations, generalized coherent states are introduced to describe the quasiclassical motion of electrons in a microwave and in a homogeneous magnetic field. The microwave is circularly polarized and propagates along the direction of the magnetic field. In view of possible applications to laboratory plasmas, the problem is treated nonrelativistically and the microwave is taken in the dipole approximation. The generalized coherent states emerge in polar coordinates (\ensuremath{\rho},\ensuremath{\varphi}) from ordinary Landau states \ensuremath{\Vert}l,m> by an appropriate choice of unitary and displacement operations. These coherent states are shown to form a complete and orthonormal set. Consequently, these states may be conveniently used for the description of scattering processes. As an example, scattering of electrons by a screened Coulomb potential is considered in the presence of the above two external fields. For simplicity, the scattering potential is treated in the first-order Born approximation. The quasiclassical features of the corresponding cross sections for the induced nonlinear processes are discussed.

Physical Review A•Jul 1, 1987•7 citations

Coherent state of an electron in a homogeneous constant magnetic field and the zero magnetic field limit

Sándor Varró

Coherent states of an electron embedded in a constant homogeneous magnetic field are constructed. The centres of the probability distributions belonging to these states gyrate along possible classical trajectories. Suitable packets of such coherent states are defined which reduce to properly normalised free electronic states in the zero magnetic field limit. A simple example is given to illustrate the dynamics of free electron localisation due to the presence of a magnetic field.

Journal of Physics A Mathematical and General•Jun 1, 1984•28 citations

On Coherent States of Relativistic Particles

I. M. Ternov, Vladislav G. Bagrov

Abstract Some general properties of coherent states of a particle in quantum mechanics are discussed and examples of relativistics coherent states of an electron moving in a steady and homogeneous field and in a non‐stationary external field of special kind are presented. In particular cases this field may be a plane wave, a Redmond field (a superposition of plane wave and homogenous magnetic field), a superposition of a Redmond field and a longitudinal electric field or other physically interesting fields.

Annalen der Physik•Jan 1, 1983•5 citations
Nonrelativistic particle in a homogeneous magnetic field was taken as an example to illustrate the general structure of quasiclassical trajectory - coherent states. Relation of these states (representing exact solutions in the case of quadratic nonrelativistic quantum systems) with widely known coherent and correlated coherent states was established.
In this paper we show that for a nonrelativistic charged particle moving in an arbitrary external electromagnetic field there exist approximate solutions of the Schrödinger equation, such that the quantum-mechanical averages of the coordinates and the momenta with respect to these states are general exact solutions of the classical Hamiltonian equations. Such states are called trajectory-coherent states. The wave functions of the trajectory-coherent states are obtained by the complex germ method by V. P. Maslov. The simplest properties of these states are studied.
By continuing earlier investigations, generalized coherent states are introduced to describe the quasiclassical motion of electrons in a microwave and in a homogeneous magnetic field. The microwave is circularly polarized and propagates along the direction of the magnetic field. In view of possible applications to laboratory plasmas, the problem is treated nonrelativistically and the microwave is taken in the dipole approximation. The generalized coherent states emerge in polar coordinates (\ensuremath{\rho},\ensuremath{\varphi}) from ordinary Landau states \ensuremath{\Vert}l,m> by an appropriate choice of unitary and displacement operations. These coherent states are shown to form a complete and orthonormal set. Consequently, these states may be conveniently used for the description of scattering processes. As an example, scattering of electrons by a screened Coulomb potential is considered in the presence of the above two external fields. For simplicity, the scattering potential is treated in the first-order Born approximation. The quasiclassical features of the corresponding cross sections for the induced nonlinear processes are discussed.
Abstract Some general properties of coherent states of a particle in quantum mechanics are discussed and examples of relativistics coherent states of an electron moving in a steady and homogeneous field and in a non‐stationary external field of special kind are presented. In particular cases this field may be a plane wave, a Redmond field (a superposition of plane wave and homogenous magnetic field), a superposition of a Redmond field and a longitudinal electric field or other physically interesting fields.