Algebraic treatment of super-integrable potentials

Details Algebraic treatment of super-integrable potentials Algebraic treatment of super-integrable potentials

2003-02-18

arxiv.org/abs/quant-ph/0302130v1

J. Math. Phys. 42 (2001) 4684 - 4707

Physics

Quantum Physics

35 pages, no figures

Scientific paper

The so$(2,1)$ Lie algebra is applied to three classes of two- and three-dimensional Smorodinsky-Winternitz super-integrable potentials for which the path integral discussion has been recently presented in the literature. We have constructed the Green's functions for two important super-integrable potentials in $R^{2}.$ Among the super-integrable potentials in $R^{3}$, we have considered two examples, one is maximally super-integrable and another one minimally super-integrable. The discussion is made in various coordinate systems. The energy spectrum and the suitably normalized wave functions of bound and continuous states are then deduced.

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