On the number of bound states in some three-parameter s-wave central potentials

Abstract

We examine some criteria for determining the existence and number of bound states for the Schrödinger equation with non-relativistic single-particle spherically symmetric potentials in three dimensions with l = 0. By analysing specific potentials described by two parameters (triangular potential) and three parameters (finite spherical shell, Woods-Saxon, and cut-off triangular potentials), we obtain functions of these parameters that determine the number of bound states in these potentials.