Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F22%3A00556198" target="_blank" >RIV/61389005:_____/22:00556198 - isvavai.cz</a>
Alternative codes found
RIV/62690094:18470/22:50019632
Result on the web
<a href="https://doi.org/10.1140/epjp/s13360-022-02567-0" target="_blank" >https://doi.org/10.1140/epjp/s13360-022-02567-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1140/epjp/s13360-022-02567-0" target="_blank" >10.1140/epjp/s13360-022-02567-0</a>
Alternative languages
Result language
angličtina
Original language name
Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians
Original language description
Even the most economical conventional formulation of quantum mechanics called Schrodinger picture (SP) need not be always computationally or conceptually optimal. A Dyson-inspired remedy can sometimes be sought in a transfer of the calculations from the conventional and correct SP Hilbert space H into a 'false but friendlier' Hilbert space R. The difference (i.e., non-equivalence) between R. and H is given by a judicious simplification of the inner product. Although the Hamiltonian H itself appears non-Hermitian in R, its necessary Hermitization (mediated by a return to H) is usually feasible. If not, another eligible remedy is described in the present paper. Our basic idea lies in the introduction of a 'chained' auxiliary manipulation multiplet of inner-product spaces R-1, R-2, ..., R-N. At arbitrary N, the structure and properties of the resulting generalized SP (GSP) formulation of quantum mechanics of unitary systems (characterized by 'hiddenly Hermitian' observables) are described and discussed in detail. Nontrivial nature of the related multi-step Dyson-map composition laws and correspondences to the conventional Hermitian models are also revealed and clarified.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
European Physical Journal Plus
ISSN
2190-5444
e-ISSN
2190-5444
Volume of the periodical
137
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
15
Pages from-to
335
UT code for WoS article
000767933400001
EID of the result in the Scopus database
2-s2.0-85126458832