Some generalizations of Volkov’s problem

Summary

Exact solutions of the Dirac equation in the presence of wave fields are considered in this work. In contrast to classical Volkov’s problem (electron in the field of plane electromagnetic wave) wave fields of various tensorial structure, namely scalar, vector (electromagnetic), tensor, pseudo-vector, pseudo-scalar fields and their superpositions are considered. There are marked situations in which exact solutions are possible without a procedure of separation of variables by means of the first-or second-order ordinary differential equations. Essential feature of the approach proposed here is the effective use of concrete representation of degenerate matrices, by means of which the problem of exact solutions of the Dirac equation may be reduced to investigation of a comparatively simple system of equations containing two ordinary differential equations and two functional-algebraic ones.