Wave Functions of Nonlocal Potentials: The Perey Effect

Abstract

An eigenfunction of an attractive nonlocal single-particle potential is always smaller inside the region of the potential than outside; the converse occurs for repulsive potentials. This is the Perey effect. In the present article explicit formulas for the effect are derived for the case of motion in one dimension, and interpretive discussions of the effect are given. The derivation does not employ series expansions. It is argued that the effect can be understood in terms of the fundamental many-body theory from which the single-particle potential has (in principle) been derived. Some of the wave function lies in the channels which have been eliminated in the course of that derivation.