SEMICLASSICAL APPROXIMATION FOR THE AVERAGE LEVEL DENSITY OF A SYSTEM OF IDENTICAL INTERACTING PARTICLES

For a system of identical particles (we take fermions as an example), we derive the analogue of the Weyl formula for the average level density. This is done by introducing the projection operator onto states in Hilbert space which have the symmetry imposed by particle identity. The semi-classical result is obtained by using the Wigner representation for this operator and by letting hBAR --> 0. Numerical examples for few degrees of freedom show in general good agreement with exact diagonalization even near the ground state.