Shape Invariance in the Calogero and Calogero-Sutherland Models

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 (6)

• Supersymmetry and Quantum Mechanics
• Exchange Operator Formalism for Integrable Systems of Particles
• Exact operator solution of the Calogero-Sutherland model
• The Calogero Model - Anyonic Representation, Fermionic Extension and Supersymmetry
• Exact Solvability of the Calogero and Sutherland Models
• Higher Dimensional SUSY Quantum Mechanics

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