Tamas Fulop, Izumi Tsutsui
A Free Particle on a Circle with Point Interaction
(47K, plain TeX)
ABSTRACT. 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 classification of the family by introducing a number of
subfamilies and thereby analyze the spectral structure in detail. We
find that the spectrum depends on a subset of U(2) parameters rather
than the entire U(2) needed for the Hamiltonians, and that in
particular there exists a subfamily in U(2) where the spectrum becomes
parameter-independent. We also show that, in some specific cases, the
WKB semiclassical approximation becomes exact (modulo phases) for the
system.