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arXiv · hep-th/9212147

New Shape Invariant Potentials in Supersymmetric Quantum Mechanics

A. Khare·U. P. Sukhatme
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Abstract

Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are reflectionless and possess an infinite number of bound states. They can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for energy eigenvalues, eigenfunctions and transmission coefficients are given. Included in our potentials as a special case is the self-similar potential recently discussed by Shabat and Spiridonov.

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A. Khare, U. P. Sukhatme. 1992-12-23. New Shape Invariant Potentials in Supersymmetric Quantum Mechanics. https://doi.org/10.1088/0305-4470%2F26%2F18%2F003

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