Closed-form propagator of the Calogero model
Quantum Physics
2025-01-30 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.2303.07231,
title = {Closed-form propagator of the Calogero model},
author = {Valdemar Melin and Edwin Langmann},
journal= {arXiv preprint arXiv:2303.07231},
year = {2025}
}
Comments
7 pages, 3 figures