Inequivalent quantization of the rational Calogero model with a Coulomb type interaction

TL;DR

This paper explores the different possible quantum formulations of a rational Calogero model with Coulomb interaction, revealing a family of solutions, new states, and ladder operators for this integrable system.

Contribution

It introduces a one-parameter family of self-adjoint extensions for the model, providing new solutions and ladder operators not previously known.

Findings

Existence of a one-parameter family of self-adjoint extensions.

Discovery of novel bound and scattering states.

Construction of ladder operators for the system.

Abstract

We consider the inequivalent quantizations of a $N$-body rational Calogero model with a Coulomb type interaction. It is shown that for certain range of the coupling constants, this system admits a one-parameter family of self-adjoint extensions. We analyze both the bound and scattering state sectors and find novel solutions of this model. We also find the ladder operators for this system, with which the previously known solutions can be constructed.