Simple unified derivation and solution of Coulomb, Eckart and Rosen-Morse potentials in prepotential approach

The four exactly solvable models related to non-sinusoidal coordinates, namely, the Coulomb, Eckart, Rosen-Morse type I and II models are normally being treated separately, despite the similarity of the functional forms of the potentials, their eigenvalues and eigenfunctions. Based on an extension o...

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Bibliographic Details
Published inAnnals of physics Vol. 324; no. 5; pp. 1095 - 1104
Main Author Ho, Choon-Lin
Format Journal Article
LanguageEnglish
Published New York Elsevier Inc 01.05.2009
Elsevier BV
Subjects
Bethe ansatz equations
COORDINATES
EIGENFUNCTIONS
EIGENVALUES
EQUATIONS
EXACT SOLUTIONS
Exact solvability
Mathematical analysis
MATHEMATICAL METHODS AND COMPUTING
Mathematical models
MORSE POTENTIAL
Prepotential
Quantum physics
Quasi-exact solvability
02.30.Ik
Prepotential
03.65.Ca
03.65.Ge
Bethe ansatz equations
Exact solvability
Quasi-exact solvability
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Summary:The four exactly solvable models related to non-sinusoidal coordinates, namely, the Coulomb, Eckart, Rosen-Morse type I and II models are normally being treated separately, despite the similarity of the functional forms of the potentials, their eigenvalues and eigenfunctions. Based on an extension of the prepotential approach to exactly and quasi-exactly solvable models proposed previously, we show how these models can be derived and solved in a simple and unified way.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2008.10.004