A Simple Tool to Study Many-Body Forces

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 H* which is solvable, the
eigenvalues of H* 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.