Singular Potentials

Abstract

This article attempts to present a comprehensive review of the literature dealing with singular potentials through March 1969. The treatment is confined principally to nonrelativistic quantum mechanics, i.e., to solutions of the partial-wave Schrödinger equation with a singular potential. Some general physical and mathematical properties are given. Exact solutions are presented for those potentials for which they are available. Techniques which have been used in obtaining approximate solutions are outlined. Formal and physical applications of singular potentials are presented. Formal applications are those for which singular potentials have served as mathematical models illustrating concepts in elementary particle physics. These include applications to the Regge pole formalism, quantum field theories, and the peratization approximation. Physical applications entail those which have been made to molecular physics and to high-energy phenomenology.