Static vortex solutions in a planar particle system obeying a generalized exclusion principle

We consider a planar particle system obeying a generalized Pauli exclusion principle. In the mean field approximation, this system is described by a S chrodinger equation we recently introduced, containing a complex nonlineari ty. The particle number, the total energy, and the angular momentum are. co nserved in such a system. We consider vortexlike stationary solutions of th e form psi (r) = rho (r)(1/2)e(in theta) and write the differential equatio n for the vortex shape. We Rnd an analytic solution of this equation and ob tain a closed expression for the vortex profile. We investigate some mean p roperties and, in particular, calculate the energy spectrum and angular mom entum of the vortex.