Relativistic quantum particle in a time-dependent homogeneous field

Abstract

Abstract A model of the relativistic quantum particle under the action of a time-dependent force is considered. This exactly solvable model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space is one-dimensional Lobachevsky space. We have explicitly constructed the wave functions and propagators for this model in both x- and p-representations. We have also found a solution of a definite class of partial differential and finite-difference equations, which can be interpreted as the operator identities.