Problem of the coexistence of several non-Hermitian observables in PT -symmetric quantum mechanics

0475655 - ÚJF 2018 RIV US eng J - Journal Article
Znojil, Miloslav - Semorádová, Iveta - Růžička, František - Moulla, H. - Leghrib, I.
Problem of the coexistence of several non-Hermitian observables in PT -symmetric quantum mechanics.
Physical Review A. Roč. 95, č. 4 (2017), č. článku 042122. ISSN 2469-9926. E-ISSN 2469-9934
R&D Projects: GA ČR GA16-22945S
Institutional support: RVO:61389005
Keywords : operators * Hilbert space * non-Hermitian
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.909, year: 2017

During recent developments in quantum theory it has been clarified that observable quantities (such as energy and position) may be represented by operators Lambda (with real spectra) that are manifestly non-Hermitian in a preselected friendly Hilbert space H-(F). The consistency of these models is known to require an upgrade of the inner product, i.e., mathematically speaking, a transition H-(F)-> H-(S) to another, standard, Hilbert space. We prove that whenever we are given more than one candidate for an observable ( i.e., say, two operators Lambda(0) and Lambda(1)) in advance, such an upgrade need not exist in general.
Permanent Link: http://hdl.handle.net/11104/0272313