Three Alternative Model-Building Strategies Using Quasi-Hermitian Time-Dependent Observables

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00575352" target="_blank" >RIV/61389005:_____/23:00575352 - isvavai.cz</a>

Alternative codes found

RIV/62690094:18470/23:50020905

Result on the web

<a href="https://doi.org/10.3390/sym15081596" target="_blank" >https://doi.org/10.3390/sym15081596</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym15081596" target="_blank" >10.3390/sym15081596</a>

Result language

angličtina

Original language name

Three Alternative Model-Building Strategies Using Quasi-Hermitian Time-Dependent Observables

Original language description

In the conventional (so-called Schrodinger-picture) formulation of quantum theory the operators of observables are chosen self-adjoint and time-independent. In the recent innovation of the theory, the operators can be not only non-Hermitian but also time-dependent. The formalism (called non-Hermitian interaction-picture, NIP) requires a separate description of the evolution of the time-dependent states ? (t) (using Schrodinger-type equations) as well as of the time-dependent observables ?(j)(t), j = 1, 2, ... , K (using Heisenberg-type equations). In the unitary-evolution dynamical regime of our interest, both of the respective generators of the evolution (viz., in our notation, the Schrodingerian generator G(t) and the Heisenbergian generator S(t)) have, in general, complex spectra. Only the spectrum of their superposition remains real. Thus, only the observable superposition H(t) = G(t) + S(t) (representing the instantaneous energies) should be called Hamiltonian. In applications, nevertheless, the mathematically consistent models can be based not only on the initial knowledge of the energy operator H(t) (forming a 'dynamical' model-building strategy) but also, alternatively, on the knowledge of the Coriolis force S(t) (forming a 'kinematical' model-building strategy), or on the initial knowledge of the Schrodingerian generator G(t) (forming, for some reason, one of the most popular strategies in the literature). In our present paper, every such choice (marked as 'one', 'two' or 'three', respectively) is shown to lead to a construction recipe with a specific range of applicability.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Symmetry-Basel

ISSN

2073-8994

e-ISSN

2073-8994

Volume of the periodical

15

Issue of the periodical within the volume

8

Country of publishing house

CH - SWITZERLAND

Number of pages

13

Pages from-to

1596

UT code for WoS article

001056629400001

EID of the result in the Scopus database

2-s2.0-85168876023