Exactly solvable model of three interacting particles in an external magnetic field

TL;DR

This paper presents an exact solution for three identical particles in a plane under a magnetic field with spring interactions, revealing quantized parameters and liquid-like correlation features.

Contribution

It provides an exact analytical model for three interacting particles in a magnetic field, including correlation functions and exchange effects, which is novel in this context.

Findings

Quantization of pair-correlation function maxima

Existence of exchange correlation hole in attractive interactions

Exact analytical expressions for mean distance and cluster area

Abstract

The quantum mechanical problem of three identical particles, moving in a plane and interacting pairwise via a spring potential, is solved exactly in the presence of a magnetic field. Calculations of the pair--correlation function, mean distance and the cluster area show a quantization of these parameters. Especially the pair-correlation function exhibits a certain number of maxima given by a quantum number. We obtain Jastrow pre-factors which lead to an exchange correlation hole of liquid type, even in the presence of the attractive interaction between the identical electrons.