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 Schrodinger equation we recently introduced, containing a complex nonlinearity. The particle number, the total energy, and the angular momentum are. conserved in such a system. We consider vortexlike stationary solutions of the form psi (r) = rho (r)(1/2)e(in theta) and write the differential equation for the vortex shape. We Rnd an analytic solution of this equation and obtain a closed expression for the vortex profile. We investigate some mean properties and, in particular, calculate the energy spectrum and angular momentum of the vortex.