Pavel Exner, Harald Grosse
Some properties of the one-dimensional generalized point
interactions (a torso)
(52K, LaTeX)
ABSTRACT. This text is a part of an unfinished project
which deals with the generalized point interaction (GPI) in one
dimension. We employ two natural parametrizations, which are
known but have not attracted much attention, to express the
resolvent of the GPI Hamiltonian as well as its spectral and
scattering properties. It is also shown that the GPI yields one
of the simplest models in which a non-trivial Berry phase is
exhibited. Furthermore, the generalized Kronig-Penney model
corresponding to the GPI is discussed. We show that there are
three different types of the high-energy behaviour for the
corresponding band spectrum.