Solution of the Spinless Salpeter Equation with a Time-Dependent Linear Potential

Abstract

We derive the general solution of the semi-relativistic spinless Salpeter equation in the presence of a time-dependent linear potential via the Lewis–Riesenfeld framework and using two forms of the invariant. For comparison, we reobtain the solution in the momentum-space directly by applying a time-momentum transformation to the involved partial differential equation. We also investigate the classical-quantum correspondence for the model in the case of time-periodic force using a momentum-space Gaussian wave-packet.