Abstract:
We establish that a perfect-transmission scattering problem can be described
by a class of parity and time reversal symmetric operators and hereby we provide
a scenario for understanding and implementing the corresponding quasi-
Hermitian quantum mechanical framework from the physical viewpoint. One of
the most interesting features of the analysis is that the complex eigenvalues of
the underlying non-Hermitian problem, associated with a reflectionless scattering
system, lead to the loss of perfect-transmission energies as the parameters
characterizing the scattering potential are varied. On the other hand, the scattering
data can serve to describe the spectrum of a large class of Schroedinger
operators with complex Robin boundary conditions. This is a common work with
David Krejcirik and Petr Siegl.
