Non-Stationary Non-Hermitian 'Wrong-Sign' Quantum Oscillators and Their Meaningful Physical Interpretation
Result description
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.
Keywords
quantum mechanics of non-stationary unitary systemsnon-Hermitian interaction representationquasi-Hermitian form of the observablesa complete set of evolution equationsinternal consistency of the probabilistic interpretationapplication to asymptotically repulsive potential models
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/62690094:18470/23:50020909
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Non-Stationary Non-Hermitian 'Wrong-Sign' Quantum Oscillators and Their Meaningful Physical Interpretation
Original language description
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.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Entropy
ISSN
1099-4300
e-ISSN
1099-4300
Volume of the periodical
25
Issue of the periodical within the volume
4
Country of publishing house
CH - SWITZERLAND
Number of pages
16
Pages from-to
692
UT code for WoS article
000980885000001
EID of the result in the Scopus database
2-s2.0-85153859442
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Applied mathematics
Year of implementation
2023