Schrödinger Equation Solutions for the Central Field Power Potential Energy II. V(r) = −V ₀(r/a ₀)^2ν−2, 0 ≤ ν ≤ 1, the Bound States

Abstract

The bound states of the generalized Schrödinger equation system with radial potential energy V(r) = −V ₀(r/a ₀)^2ν−2, 0 ≤ ν ≤ 1, are described. The solutions of the differential equation are related to the functions for the bound state problem with ν ≥ 1. The Green's function is constructed as well as its first iteration, the traces of both functions are calculated, and an upper and lower bound for the ground state is established. A WKB-like approximate solution for the eigenvalues and eigenfunctions is derived.