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5 papers · 2 filters
Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials
S. Odake, R. Sasaki
We show that the equilibrium positions of the Ruijsenaars-Schneider-van Diejen systems with the trigonometric potential are given by the zeros of the Askey-Wilson polynomials with…
Shape Invariant Potentials in "Discrete Quantum Mechanics"
S. Odake, R. Sasaki
Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant ``discrete quantum mechanical systems" are introduced an…
Polynomials Associated with Equilibria of Affine Toda-Sutherland Systems
S. Odake, R. Sasaki
An affine Toda-Sutherland system is a quasi-exactly solvable multi-particle dynamics based on an affine simple root system. It is a `cross' between two well-known integrable multi-…
Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials
S. Odake, R. Sasaki
The Ruijsenaars-Schneider systems are `discrete' version of the Calogero-Moser (C-M) systems in the sense that the momentum operator p appears in the Hamiltonians as a polynomial i…
Generalized Heisenberg's Dynamics
Yoshiharu Kawamura
We formulate a dynamical system based on many-index objects. These objects yield a generalization of the Heisenberg's equation. Systems describing harmonic oscillators are given.