Supersymmetry,Shape Invariance and Exactly Solvable Noncentral Potentials

Abstract

Using the ideas of supersymmetry and shape invariance we show that the eigenvalues and eigenfunctions of a wide class of noncentral potentials can be obtained in a closed form by the operator method. This generalization considerably extends the list of exactly solvable potentials for which the solution can be obtained algebraically in a simple and elegant manner. As an illustration, we discuss in detail the example of the potential $$V(r,\theta ,\varphi )=\frac{{\omega }^2}{4}{r}^2+\frac{\delta }{r^2}+\frac{C}{r^{2}si{n}^2\theta }+\frac{D}{r^{2}co{s}^2\theta }+\frac{F}{r^{2}si{n}^2\theta si{n}^2\alpha \varphi }+\frac{G}{r^{2}si{n}^2\theta co{s}^2\alpha \varphi }$$ with 7 parameters.Other algebraically solvable examples are also given.

16 pages

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