Analytic, group-theoretic wave functions for confined, correlated N-body systems with general two-body interactions

In this paper, we develop an analytic N-body wave function for identical particles under quantum confinement with a general two-body interaction. A systematic approach to correlation is developed by combining three theoretical methods: dimensional perturbation theory, the FG method of Wilson et. al., and the group theory of the symmetric group. Analytic results are achieved for a completely general interaction potential. Unlike conventional perturbation methods which are applicable only for weakly interacting systems, this analytic approach is applicable to both weakly and strongly interacting systems. This method directly accounts for each two-body interaction, rather than an average interaction so even lowest-order results include beyond-mean-field effects. One major advantage is that N appears as a parameter in the analytical expressions for the energy so results for different N are easy to obtain.