Shape Invariant Potentials in "Discrete Quantum Mechanics"

Details Shape Invariant Potentials in "Discrete Quantum Mechanics" Shape Invariant Potentials in "Discrete Quantum Mechanics"

2004-10-10

arxiv.org/abs/hep-th/0410102v1

J.Nonlin.Math.Phys. 12 (2005) S507-S521

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 1 figure. Contribution to a special issue of Journal of Nonlinear Mathematical Physics in honour of Francesco Caloge

Scientific paper

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.

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