Abstract
A discussion is given of the problem of a charged particle in a transverse electromagnetic plane wave. The symmetry of the potential and of the equations of motion is determined. The conserved quantities and the invariant operators are used to solve the equations of motion. As is well known these equations are exactly solvable. Here it is shown how these solutions can be obtained by group-theoretical methods. The irreducible co-representations of the symmetry groups are given and the corresponding selection rules discussed. It is shown that the Klein-Gordon are Dirac equations can be treated in quite the same way as the time-independent Schrödinger equation for a charged particle in a crystal. Such a treatment leads in a natural way to four-dimensional crystallographic notions and to concepts like mass bands and effective mass.
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