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Communications in Nonlinear Science and Numerical Simulation

A semi-inverse variational method for generating the bound state energy eigenvalues in a quantum system: The Schrödinger equation

Abdelwahab Zerarka, K. Libarir

Published Dec 7, 2008• 18 citations
Publisher
DOI
10.1016/j.cnsns.2008.11.008

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A method for systematically improving Hall–Post–Stenschke lower bounds to the bound state eigenvalues of three-body Schrödinger equations is given. The improved bounds are obtained by solving coupled one variable integral equations; the bounds get better as the number of coupled equations is increased. The method generates explicit wave functions which can be used to obtain complementary upper bounds via the Rayleigh–Ritz variational method. Either identical or nonidentical particles can be handled. The method is illustrated by calculations for three identical particles bound by Hooke’s law forces. A brief discussion of extensions to more than three particles is given.