Calogero-Sutherland Type Models in Higher Dimensions

TL;DR

This paper introduces two new higher-dimensional Calogero-Sutherland models with two-body interactions, providing exact wave functions and ground states for any number of spinless particles.

Contribution

It presents novel higher-dimensional Calogero-Sutherland models with exact solutions, expanding the understanding of integrable many-body systems.

Findings

Derived exact wave functions for the models

Obtained ground state solutions for arbitrary particle numbers

Extended Calogero-Sutherland models to higher dimensions

Abstract

We construct two different Calogero-Sutherland type models with only two-body interactions in arbitrary dimensions. We obtain some exact wave functions, including the ground states, of these two models for arbitrary number of spinless nonrelativistic particles.