On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators
Publisher DOI
Abstract
We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.
Date Issued
2014
Publication Type
Article
Subject(s)
Language(s)
en
Author(s)
Železný, Jakub | |
Krejčiřík, David |
Additional Credits
Journal
Complex analysis and operator theory
Publisher
Birkhäuser
ISSN
1661-8254
Access(Rights)
open.access