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.