Shape Invariance in the Calogero and Calogero-Sutherland Models
arXiv:quant-ph/9702017 · doi:10.1103/PhysRevA.56.208
Abstract
We show that the Calogero and Calogero-Sutherland models possess an N-body generalization of shape invariance. We obtain the operator representation that gives rise to this result, and discuss the implications of this result, including the possibility of solving these models using algebraic methods based on this shape invariance. Our representation gives us a natural way to construct supersymmetric generalizations of these models, which are interesting both in their own right and for the insights they offer in connection with the exact solubility of these models.
Latex file, 23 pages, no pictures
References in corpus (1)
Cited by in corpus (16)
- A Quantum Exactly Solvable Nonlinear Oscillator with quasi-Harmonic Behaviour
- Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
- Quantum Calogero-Moser Models: Integrability for all Root Systems
- Quantum vs Classical Integrability in Calogero-Moser Systems
- Supersymmetry, Shape Invariance and Solvability of and Calogero-Sutherland Model
- Super-Calogero-Moser-Sutherland systems and free super-oscillators : a mapping
- Multiparticle SUSY quantum mechanics and the representations of permutation group
- Super-Calogero model with OSp(2|2) supersymmetry : is the construction unique?
- Intertwining Relations for the Matrix Calogero-like Models: Supersymmetry and Shape Invariance
- Exactly Solvable Three-body SUSY Systems with Internal Degrees of Freedom
- Quasi exactly solvable extension of Calogero model associated with exceptional orthogonal polynomials
- New Two-Dimensional Quantum Models with Shape Invariance
- Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
- Two-particle Wigner functions in a one-dimensional Calogero-Sutherland potential
- Algebraic integrability of -deformed Calogero models
- Equivalence of the super Lax and local Dunkl operators for Calogero-like models