Schrodinger Equation Solutions for the Central Field Power Potential Energy I. V(r) = V .sub.0(r/a .sub.0).sup.2I1/2-2, I1/2 aY= 1

Byline: Paul Caylor McKinney (1) Keywords: Schrodinger equation; eigenfunctions; eigenvalues; Green's function; WKB approximation; central field power potential energy Abstract: The solution of a generalized non-relativistic Schrodinger equation with radial potential energy V(r)=V .sub.0(r/a .sub.0).sup.2I1/2-2 is presented. After reviewing the general properties of the radial ordinary differential equation, power series solutions are developed. The Green's function is constructed, its trace and the trace of its first iteration are calculated, and the ability of the traces to provide upper and lower bounds for the ground eigenvalue is examined. In addition, WKB-like solutions for the eigenvalues and eigenfunctions are derived. The approximation method yields valid eigenvalues for large quantum numbers (Rydberg states). Author Affiliation: (1) Department of Chemistry, Wabash College, P.O. Box 352, Crawfordsville, IN, 47933-0352, USA Article History: Registration Date: 09/10/2004