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Advances in High Energy Physics
Volume 2018, Article ID 7906536, 12 pages
https://doi.org/10.1155/2018/7906536
Research Article

Hermitian–Non-Hermitian Interfaces in Quantum Theory

Nuclear Physics Institute of the CAS, 250 68 Řež, Czech Republic

Correspondence should be addressed to Miloslav Znojil; zc.sac.fju@lijonz

Received 10 January 2018; Accepted 18 February 2018; Published 24 April 2018

Academic Editor: Saber Zarrinkamar

Copyright © 2018 Miloslav Znojil. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

In the global framework of quantum theory, the individual quantum systems seem clearly separated into two families with the respective manifestly Hermitian and hiddenly Hermitian operators of their Hamiltonian. In the light of certain preliminary studies, these two families seem to have an empty overlap. In this paper, we will show that whenever the interaction potentials are chosen to be weakly nonlocal, the separation of the two families may disappear. The overlaps alias interfaces between the Hermitian and non-Hermitian descriptions of a unitarily evolving quantum system in question may become nonempty. This assertion will be illustrated via a few analytically solvable elementary models.