Quantum Inverse Square Interaction

TL;DR

This paper explores the mathematical structure and applications of inverse square interaction Hamiltonians, focusing on the N-body Calogero model and its recently discovered solutions.

Contribution

It provides an analysis of the N-body Calogero model, highlighting novel solutions and their properties within the context of inverse square interactions.

Findings

Identification of new solutions to the Calogero model

Analysis of the mathematical structure of inverse square Hamiltonians

Discussion of applications in physical systems

Abstract

Hamiltonians with inverse square interaction potential occur in the study of a variety of physical systems and exhibit a rich mathematical structure. In this talk we briefly mention some of the applications of such Hamiltonians and then analyze the case of the N-body rational Calogero model as an example. This model has recently been shown to admit novel solutions, whose properties are discussed.