Siegl, Petr; Železný, Jakub; Krejčiřík, David (2014). On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators. Complex analysis and operator theory, 8(1), pp. 255-281. Birkhäuser 10.1007/s11785-013-0301-y
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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.
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Siegl, Petr |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1661-8254 |
Publisher: |
Birkhäuser |
Language: |
English |
Submitter: |
Mario Amrein |
Date Deposited: |
14 Apr 2015 15:51 |
Last Modified: |
05 Dec 2022 14:45 |
Publisher DOI: |
10.1007/s11785-013-0301-y |
BORIS DOI: |
10.7892/boris.66714 |
URI: |
https://boris.unibe.ch/id/eprint/66714 |
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