Analytic, Group-Theoretic Wave Functions for Confined N-Body Quantum   Systems
  Systems involving N-identical interacting particles under quantum confinement appear in many areas of physics, including chemical, condensed matter, and atomic physics. We discuss a beyondmean- field perturbation method that is applicable to weakly, intermediate and strongly-interacting systems. Group theory is used to derive an analytic beyond-mean-field correlated wave function at zeroth order for a system under spherical confinement. We derive the corresponding zeroth-order analytic density profile and apply it to the example of a Bose-Einstein condensate. 
W.B. Laing, M. Dunn, J.G. Loeser, and D.K. Watson