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Annalen der Physik

On Coherent States of Relativistic Particles

I. M. Ternov, Vladislav G. Bagrov

Published Jan 1, 1983• 5 citations
Publisher

Abstract

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.

DOI
10.1002/andp.19834950102

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We study the classification of electromagnetic fields using the equivalence relation on the set of all 4-potentials of the Schrodinger equation. In the general case we find the relations among the equivalent fields, currents, and charge densities. Particularly, we study the fields equivalent to the null field. We show that the non-stationary state function for a particle in arbitrary uniform time-dependent magnetic field is equivalent to a plane wave. We present that the known coherent states of a free particle are equivalent to the stationary states of an isotropic oscillator. We reveal that the only constant magnetic field is not equivalent to the null field (contrary to a constant electrical field) and we find other fields that are equivalent to the constant magnetic field. We establish that one particular transformation of the free Schrodinger equation puts a plane wave and Green's function in a equivalence relation. c

•Jan 1, 2008•0 citations
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.
Abstract In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and continuous spectra. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space appropriate for building the related coherent states. These latter are achieved in the context where we consider both spectra purely discrete obeying the criteria that a family of coherent states must satisfy.
In the present work we construct coherent states in the magnetic–solenoid field, which is a superposition of the Aharonov–Bohm field and a collinear uniform magnetic field. In the problem under consideration there are two kinds of coherent states, those which correspond to classical trajectories which embrace the solenoid and those which do not. The constructed coherent states reproduce exactly classical trajectories, maintain their form under the time evolution and form a complete set of functions, which can be useful in semiclassical calculations. In the absence of the solenoid field these states are reduced to the well known in the case of uniform magnetic field Malkin–Man'ko coherent states.
We study the classification of electromagnetic fields using the equivalence relation on the set of all 4-potentials of the Schrodinger equation. In the general case we find the relations among the equivalent fields, currents, and charge densities. Particularly, we study the fields equivalent to the null field. We show that the non-stationary state function for a particle in arbitrary uniform time-dependent magnetic field is equivalent to a plane wave. We present that the known coherent states of a free particle are equivalent to the stationary states of an isotropic oscillator. We reveal that the only constant magnetic field is not equivalent to the null field (contrary to a constant electrical field) and we find other fields that are equivalent to the constant magnetic field. We establish that one particular transformation of the free Schrodinger equation puts a plane wave and Green's function in a equivalence relation. c