 99390 Pavel Exner, Harald Grosse
 Some properties of the onedimensional generalized point
interactions (a torso)
(52K, LaTeX)
Oct 19, 99

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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 nontrivial Berry phase is
exhibited. Furthermore, the generalized KronigPenney model
corresponding to the GPI is discussed. We show that there are
three different types of the highenergy behaviour for the
corresponding band spectrum.
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