Supersymmetry,Shape Invariance and Exactly Solvable Noncentral Potentials

Details Supersymmetry,Shape Invariance and Exactly Solvable Noncentral Potentials Supersymmetry,Shape Invariance and Exactly Solvable Noncentral Potentials

1993-10-16

arxiv.org/abs/hep-th/9310104v1

Am.J.Phys. 62 (1994) 1008-1014

Physics

High Energy Physics

High Energy Physics - Theory

16 pages

Scientific paper

10.1119/1.17698

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 $$V(r,\theta,\phi)={\omega^2\over 4}r^2 + {\delta\over r^2}+{C\over r^2 sin^2\theta}+{D\over r^2 cos^2\theta} + {F\over r^2 sin^2\theta sin^2 \alpha\phi} +{G\over r^2 sin^2\theta cos^2\alpha\phi}$$ with 7 parameters.Other algebraically solvable examples are also given.

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