arXiv:1211.1895 · Advances in Theoretical and Mathematical Physics
A new approach to the -particle problem in QM
Joachim Schröter
Abstract
In this paper the old problem of determining the discrete spectrum of a multi-particle Hamiltonian is reconsidered.The aim is to bring a fermionic Hamiltonian for arbitrary numbers N of particles by analytical means into a shape such that modern numerical methods can successfully be applied.For this purpose the Cook-Schroeck Formalism is taken as starting point.This includes the use of the occupation number representation.It is shown that the N -particle Hamiltonian is determined in a canonical way by a fictional 2particle Hamiltonian.A special approximation of this 2-particle operator delivers an approximation of the N -particle Hamiltonian, which is the orthogonal sum of finite dimensional operators.A complete classification of the matrices of these operators is given.Finally the method presented here is formulated as a work program for practical applications.The connection with other methods for solving the same problem is discussed.