Quantum propagator for some classes of three-dimensional three-body systems

TL;DR

This paper derives exact solutions for three-dimensional three-body propagators with quadratic interactions, applicable to various masses and couplings, using Feynman path integrals, and retrieves energy spectra and eigenfunctions.

Contribution

It provides the first exact analytical solutions for a broad class of three-body propagators with quadratic interactions in three dimensions.

Findings

Exact propagators for quadratic three-body systems derived

Energy spectra and eigenfunctions obtained from propagators

Applicable to systems with arbitrary masses and couplings

Abstract

In this work we solve exactly a class of three-body propagators for the most general quadratic interactions in the coordinates, for arbitrary masses and couplings. This is done both for the constant as the time-dependent couplings and masses, by using the Feynman path integral formalism. Finally the energy spectrum and the eigenfunctions are recovered from the propagators.