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Journal of Mathematical Physics

On a time-dependent extension of the Morse potential

Anne E. Kondo, D. Rodney Truax

Published Jun 1, 1988• 17 citations
Publisher

Abstract

A time-dependent extension of a Morse potential is formulated. Both the bound and unbound state wave functions are obtained algebraically for the resulting time-dependent Schrödinger equations, based upon the representations of su(2) and su(1,1), respectively. The method of R-separation of variables is instrumental in the analysis.
DOI
10.1063/1.527932

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In this paper, Schrodinger equation has been solved analytically with position dependent mass by the Rosen-Morse potential. The position dependent mass defined as the function 1/(1 — tanh(η x )). Then corresponding position dependent mass substituted into Schrodinger equation. After that the obtained equation compared with associated Jacobi differential equation. Therefore, the eigenvalue and eigenfunctionhave been calculated, and from there the bound state has been found in terms of quantum numbers and the coefficients of potential. Also, the wave function has been obtained in terms of the associated Jacobi equation by μ = —3 and v = 2.