On the Thomas-Fermi approximation for Bose condensates in traps

Thomas-Fermi theory for Bose condesates in inhomogeneous traps is revisited. The phase-space distribution function in the Thomas-Fermi limit is $f_0(\bold{R},\bold{p})$ $\alpha$ $\delta(\mu - H_{cl})$ where $H_{cl}$ is the classical counterpart of the self-consistent Gross-Pitaevskii Hamiltonian. No assumption on the large N-limit is introduced and, e.g the kinetic energy is found to be in good agreement with the quantal results even for low and intermediate particle numbers N. The attractive case yields conclusive results as well.