Volkov solutions for relativistic quantum plasmas

This work studies the electron quantum states, as determined by the Dirac equation, in the field of electrostatic and electromagnetic waves in a plasma. We discuss the main differences with respect to the vacuum case, and the assumptions under which the vacuum Volkov solutions can be adapted to a plasma. The case of ultrashort electromagnetic wave pulses is also discussed. We also consider the electron states in the field of an electron plasma wave. Modified Volkov solutions of the Dirac equation can also be found. For electron plasma waves such that the phase velocity becomes close to the speed of light, these solutions are exact. Finally, we consider electron states in the field of two waves in a plasma, with relevance to the mixed case where one of the waves is electrostatic and the other is electromagnetic.