Extending the four-body problem of Wolfes to non-translationally invariant interactions

TL;DR

This paper extends the four-body Wolfes model by incorporating non-translationally invariant interactions, providing exact solutions in one and higher dimensions, and analyzing the physical acceptability of solutions based on coupling constants.

Contribution

It introduces a novel exactly solvable four-body quantum model with non-translationally invariant potentials and generalizes the solutions to arbitrary dimensions.

Findings

Exact eigensolutions for the extended four-body system

Energy spectrum characterized for different coupling regimes

Identification of conditions for physically acceptable solutions

Abstract

We propose and solve exactly the Schr\"odinger equation of a bound quantum system consisting in four particles moving on a real line with both translationally invariant four particles interactions of Wolfes type \cite{Wolf74} and additional non translationally invariant four-body potentials. We also generalize and solve exactly this problem in any $D$-dimensional space by providing full eigensolutions and the corresponding energy spectrum. We discuss the domain of the coupling constant where the irregular solutions becomes physically acceptable