An exactly solvable three-particle problem with three-body interaction

TL;DR

This paper presents an exactly solvable three-particle quantum problem with three-body interactions, revealing its spectrum, wave functions in terms of Jack polynomials, and underlying sl(3,R) symmetry.

Contribution

It introduces a new exactly solvable model with three-body interactions and uncovers its hidden algebraic symmetry, expanding the class of solvable quantum many-body systems.

Findings

Derived the energy spectrum of the three-body Hamiltonian.

Expressed wave functions using Jack polynomials.

Identified hidden sl(3,R) symmetry explaining solvability.

Abstract

The energy spectrum of the three-particle Hamiltonian obtained by replacing the two-body trigonometric potential of the Sutherland problem by a three-body one of a similar form is derived. When expressed in appropriate variables, the corresponding wave functions are shown to be expressible in terms of Jack polynomials. The exact solvability of the problem with three-body interaction is explained by a hidden sl(3,\R) symmetry.