Multi-Particle Quasi Exactly Solvable Difference Equations
arXiv:0708.0716 · doi:10.1063/1.2818561
Abstract
Several explicit examples of multi-particle quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable multi-particle Hamiltonians, the Ruijsenaars-Schneider-van Diejen systems. These are difference analogues of the quasi exactly solvable multi-particle systems, the quantum Inozemtsev systems obtained by deforming the well-known exactly solvable Calogero-Sutherland systems. They have a finite number of exactly calculable eigenvalues and eigenfunctions. This paper is a multi-particle extension of the recent paper by one of the authors on deriving quasi exactly solvable difference equations of single degree of freedom.
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References in corpus (8)
- Shape Invariant Potentials in "Discrete Quantum Mechanics"
- Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials
- Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials
- Quasi Exactly Solvable Difference Equations
- Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials
- Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics
- Deformed multi-variable Fokker-Planck equations
- Deformed Fokker-Planck Equations
Cited by in corpus (8)
- Orthogonal Polynomials from Hermitian Matrices
- Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
- Orthogonal Polynomials from Hermitian Matrices II
- Quasi Exactly Solvable Difference Equations
- Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism
- New Quasi Exactly Solvable Difference Equation
- Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
- Exactly and quasi-exactly solvable `discrete' quantum mechanics