Shape invariance in the Calogero and Calogero-Sutherland models

1997/02/06 by Costas Efthimiou, Donald Spector · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #cond-mat #hep-th #quant-ph

paper · pdf · doi:10.1103/physreva.56.208

Latex file, 23 pages, no pictures

arxiv created 1997/02/06 · openalex publication_date 1997/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Exchange operator formalism for integrable systems of particles
• Exact operator solution of the Calogero-Sutherland model
• EXACT SOLVABILITY OF THE CALOGERO AND SUTHERLAND MODELS
• Supersymmetry and Quantum Mechanics

Cited by

• Quasi exactly solvable extension of Calogero model associated with exceptional orthogonal polynomials
• A quantum exactly solvable non-linear oscillator with quasi-harmonic behaviour