New Shape Invariant Potentials in Supersymmetric Quantum Mechanics

Details New Shape Invariant Potentials in Supersymmetric Quantum Mechanics New Shape Invariant Potentials in Supersymmetric Quantum Mechanics

1992-12-23

arxiv.org/abs/hep-th/9212147v1

J.Phys. A26 (1993) L901-L904

Physics

High Energy Physics

High Energy Physics - Theory

8pages, TeX

Scientific paper

10.1088/0305-4470/26/18/003

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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