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Bulletin of the American Physical Society

Charges in an electromagnetic wave directed along a constant magnetic field: quantum and classical solutions

W. E. Baylis, Renán Cabrera

Published May 19, 2006• 0 citations
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Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.
We deal with the motion of a charged particle in a constant magnetic field when immersed in a medium that exerts some type of friction. We analyse the problem classically and also quantum mechanically. In the latter case we use coherent state solutions of the problem that, for large energies, compared with the one associated with the cyclotron frequency, reduce to the classical limit. To study the dynamical behaviour we use time-dependent wave packets that can be constructed by superposition of the coherent states.