Fractional and integer angular momentum wavefunctions localized on classical orbits: the case of E = 0

Abstract

In two-dimensional space, where the intermediate statistics between bosons and fermions are possible, we study a localization of some stationary coherent states on classical orbits in the potentials V(r) = −γν/rν, γν > 0 for the total energy E = 0. It is shown that excellent quantum-classical correspondence can be reached for two large classes of classical orbits with ν < −2 (open curves) and with ν > 2 (closed curves). To that purpose, it was necessary to introduce fractional angular momenta for some values of ν. They are a consequence of imposing special boundary conditions on the used wavefunctions.