Shape Invariant Potentials in "Discrete Quantum Mechanics"
arXiv:hep-th/0410102 · doi:10.2991/jnmp.2005.12.s1.41
Abstract
Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant ``discrete quantum mechanical systems" are introduced and discussed in some detail. They arise in the problem of describing the equilibrium positions of Ruijsenaars-Schneider type systems, which are "discrete" counterparts of Calogero and Sutherland systems, the celebrated exactly solvable multi-particle dynamics. Deformed Hermite and Laguerre polynomials are the typical examples of the eigenfunctions of the above shape invariant discrete quantum mechanical systems.
15 pages, 1 figure. Contribution to a special issue of Journal of Nonlinear Mathematical Physics in honour of Francesco Calogero on the occasion of his seventieth birthday
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