|
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 Schrödinger operators with complex Robin boundary conditions. The talk is based on a joint work with Hector Hernandez-Corronado (FNSPE CTU in Prague) and David Krejcirik (NPI AS CR, Rez & BCAM, Bilbao). A preprint is available at arXiv:1011.4281. |
|