Interaction of a Nonrelativistic Particle with a Scalar Field with Application to Slow Electrons in Polar Crystals

Abstract

A general variational technique is developed to study the effect of recoil on the motion of a nonrelativistic particle in a scalar field. The ground-state energy is determined, and the results obtained are shown to be exact in the limit of both weak and strong field-particle coupling. This method is applied to investigate the low-lying energy levels of a conduction electron in a polar crystal. The ground-state energy and effective mass so obtained are shown to be in good agreement with the results of Lee, Low, and Pines for the intermediate coupling strengths occurring in real polar crystals.