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Schrödinger Equation Solutions for the Central Field Power Potential Energy I. V(r) = V 0(r/a 0)2ν−2, ν ≥ 1

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Abstract

The solution of a generalized non-relativistic Schrödinger equation with radial potential energy V(r)=V 0(r/a 0)2ν−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).

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  1. Department of Chemistry, Wabash College, P.O. Box 352, Crawfordsville, IN, 47933-0352, USA

    Paul Caylor McKinney

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  1. Paul Caylor McKinney
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McKinney, P.C. Schrödinger Equation Solutions for the Central Field Power Potential Energy I. V(r) = V 0(r/a 0)2ν−2, ν ≥ 1. Journal of Mathematical Chemistry 32, 381–404 (2002). https://doi.org/10.1023/A:1022905606550

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