Thomas Fermi approximation and large-$N$ quantum mechanics

Abstract

We note that the Thomas Fermi limit of Gross Pitaevskii equation and $N>>1$ limit of quantum mechanics, where $N$ is the dimensionality of space, are based on the same point of view. We combine these two to produce a modified Thomas Fermi approximation which gives a very good account of the energy of the condensate in harmonic trap.