Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics

Details Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics

2005-05-09

arxiv.org/abs/hep-th/0505070v1

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, 1 figure. Contribution to proceedings of RIMS workshop "Elliptic Integrable Systems" (RIMS, Nov. 2004)

Scientific paper

Certain aspects of the integrability/solvability of the Calogero-Sutherland-Moser systems and the Ruijsenaars-Schneider-van Diejen systems with rational and trigonometric potentials are reviewed. The equilibrium positions of classical multi-particle systems and the eigenfunctions of single-particle quantum mechanics are described by the same orthogonal polynomials: the Hermite, Laguerre, Jacobi, continuous Hahn, Wilson and Askey-Wilson polynomials. The Hamiltonians of these single-particle quantum mechanical systems have two remarkable properties, factorization and shape invariance.

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