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Physica

Coherent states of a charged particle in a time-dependent uniform electromagnetic field of a plane current

V. V. Dodonov, I.A. Malkin, Vladimir I. Man’ko

Published May 1, 1972• 63 citations
Publisher
DOI
10.1016/0031-8914(72)90082-1

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Classification of Electromagnetic Fields in non-Relativist Mechanics

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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
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