Intertwining Relations for the Matrix Calogero-like Models: Supersymmetry and Shape Invariance

Abstract

Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation) differential operators. These operators intertwine the matrix Hamiltonians corresponding to irreducible representations of the permutation group $S_N$. In particular cases, this method allows to construct a new class of exactly solvable Dirac-like equations and a new class of matrix models with shape invariance. The connection with approach of multidimensional supersymmetric quantum mechanics is established.

24 p.p

References in corpus (5)

• General Forms of a N-fold Supersymmetric Family
• New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance
• Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry
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Cited by in corpus (10)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• The spherical sector of the Calogero model as a reduced matrix model
• Exact Solvability of Two-Dimensional Real Singular Morse Potential
• Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models
• New Two-Dimensional Quantum Models with Shape Invariance
• Multidimensional quasi-exactly solvable potentials with two known eigenstates
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Supersymmetrical Separation of Variables for Scarf II Model: Partial Solvability
• Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane
• Equivalence of the super Lax and local Dunkl operators for Calogero-like models