The wave function of free electron in a strong laser plasma is obtained by solving exactly the Dirac equation in a curved space-time with optical metric for the laser plasma.

A class of exact solutions of the Dirac equation are obtained for an electron in the electromagnetic field of a wave guide formed by two pairs of hyperbolic cylinders.

Secondly, we investigate the energy density produced by a state vector which is the superposition of three single electron states in the Dirac field in the four-dimensional Minkowski spacetime.