EXACT PROPAGATOR FOR AN ELECTRON IN A UNIFORM ELECTRIC FIELD AND ITS APPLICATION TO STARK EFFECT CALCULATIONS

A calculation is presented of the single-particle propagator for a free electron in a uniform electric field. In its time-dependent form this takes simple closed forms in both momentum and configuration space. Series expansions for the Fourier transform of the configuration-space propagator are given. Using the latter a calculation is made of the electric-field dependence of the (approximate) bound state of the delta-function potential. A variational method which is suitable for general potentials is also given.