A free particle on a circle with point interaction

The quantum dynamics of a free particle on a circle with point interaction is described by a U(2) family of self-adjoint Hamiltonians. We provide a cl assification of the family by introducing a number of subfamilies and there by analyze the spectral structure in detail. We find that the spectrum depe nds on a subset of U(2) parameters rather than the entire U(2) needed for t he Hamiltonians. and that in particular there exists a subfamily in U(2) wh ere the spectrum becomes parameter-independent. We also show that, in some specific cases, the WKB semiclassical approximation becomes exact (modulo p hases) for the system. (C) 2000 Published by Elsevier Science B.V. All righ ts reserved.