Closed-form propagator of the Calogero model

Abstract

We present an exact closed-form expression for the propagator of the Calogero model, i.e., for the integral kernel of the time evolution operator of the quantum many-body system on the real line with an external harmonic potential and inverse-square two-body interactions. This expression is obtained by combining two results: first, a simple formula relating this propagator to the eigenfunctions of the Calogero model without harmonic potential and second, a formula for these eigenfunctions as finite sums of products of polynomial two-body functions.

arXiv comment7 pages, 3 figures

References in corpus (6)

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• Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators
• Explicit Solution to the N-Body Calogero Problem
• A Conjecture about Raising Operators for Macdonald Polynomials
• Explicit formulas for the eigenfunctions of the N-body Calogero model
• Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence