A Simple Tool to Study Many-Body Forces

Abstract

The envelope theory, also known as the auxiliary field method, is a technique to compute approximate solutions of a quantum system with N identical particles. The basic idea is to replace the Hamiltonian H under study by an auxiliary Hamiltonian (formula presented) which is solvable, the eigenvalues of (formula presented) being optimized to be as close as possible to those of H. The method is easy to implement since it reduces to find the solution of a transcendental equation. We show here that the envelope theory can be extended to compute the eigensolutions of a system of identical particles with a type of many-body forces often used in phenomenological models.