Energy spectrum of interacting gas: cluster expansion method

TL;DR

This paper introduces a novel approach to compute the energy spectrum of interacting gases by adapting the cluster expansion method into an eigenvalue solving technique, enabling direct calculation from interparticle potentials.

Contribution

It presents an explicit formula for energy eigenvalues of interacting gases, bridging statistical mechanics and quantum eigenvalue problems, demonstrated with soft-sphere potentials.

Findings

Derived explicit energy eigenvalue expression for interacting gases

Enabled direct calculation from interparticle potentials

Applied method successfully to soft-sphere potential model

Abstract

In this paper, we calculate the energy spectrum of interacting gases by converting the cluster expansion method in statistical mechanics into a method of solving energy eigenvalues. We obtain an explicit expression of the energy eigenvalue, by which we can calculate the eigenvalue of an interacting gas from the interparticle potential directly. As an example, we calculate the energy spectrum for an interacting gas with soft-sphere potentials.