Non-Stationary Non-Hermitian 'Wrong-Sign' Quantum Oscillators and Their Meaningful Physical Interpretation

0571840 - ÚJF 2024 RIV CH eng J - Journal Article
Znojil, Miloslav
Non-Stationary Non-Hermitian 'Wrong-Sign' Quantum Oscillators and Their Meaningful Physical Interpretation.
Entropy. Roč. 25, č. 4 (2023), č. článku 692. E-ISSN 1099-4300
Institutional support: RVO:61389005
Keywords : quantum mechanics of non-stationary unitary systems * non-Hermitian interaction representation * quasi-Hermitian form of the observables * a complete set of evolution equations * internal consistency of the probabilistic interpretation * application to asymptotically repulsive potential models
OECD category: Applied mathematics
Impact factor: 2.7, year: 2022
Method of publishing: Open access
https://doi.org/10.3390/e25040692

In the framework of quantum mechanics using quasi-Hermitian operators the standard unitary evolution of a non-stationary but still closed quantum system is only properly described in the non-Hermitian interaction picture (NIP). In this formulation of the theory both the states and the observables vary with time. A few aspects of implementation of this picture are illustrated via the 'wrong-sign' quartic oscillators. It is shown that in contrast to the widespread belief, both of the related Schrodinger-equation generators G(t) and the Heisenberg-equation generators s(t) are just auxiliary concepts. Their spectra are phenomenologically irrelevant and, in general, complex. It is argued that only the sum H(t)=G(t)+s(t) of the latter operators retains the standard physical meaning of the instantaneous energy of the unitary quantum system in question.
Permanent Link: https://hdl.handle.net/11104/0342753