Shape Invariant Potentials in "Discrete Quantum Mechanics"
摘要
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.
引用
@article{arxiv.hep-th/0410102,
title = {Shape Invariant Potentials in "Discrete Quantum Mechanics"},
author = {S. Odake and R. Sasaki},
journal= {arXiv preprint arXiv:hep-th/0410102},
year = {2015}
}
备注
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