Three-Hilbert-Space Formulation of Quantum Mechanics

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Three-Hilbert-Space Formulation of Quantum Mechanics

Popis výsledku v původním jazyce

In paper [Znojil M., Phys. Rev. D 78 (2008), 085003, 5 pages, arXiv: 0809.2874] the two-Hilbert-space (2HS, a.k.a. cryptohermitian) formulation of Quantum Mechanics has been revisited. In the present continuation of this study (with the spaces in question denoted as H-(auxiliary) and H-(standard)) we spot a weak point of the 2HS formalism which lies in the double role played by H-(auxiliary). As long as this confluence of roles may (and did!) lead to confusion in the literature, we propose an amended, three-Hilbert-space (3HS) reformulation of the same theory. As a byproduct of our analysis of the formalism we offer an amendment of the Dirac's bra-ket notation and we also show how its use clarifies the concept of covariance in time-dependent cases. Viaan elementary example we finally explain why in certain quantum systems the generator H-(gen) of the time-evolution of the wave functions may differ from their Hamiltonian H.

Název v anglickém jazyce

Three-Hilbert-Space Formulation of Quantum Mechanics

Popis výsledku anglicky

In paper [Znojil M., Phys. Rev. D 78 (2008), 085003, 5 pages, arXiv: 0809.2874] the two-Hilbert-space (2HS, a.k.a. cryptohermitian) formulation of Quantum Mechanics has been revisited. In the present continuation of this study (with the spaces in question denoted as H-(auxiliary) and H-(standard)) we spot a weak point of the 2HS formalism which lies in the double role played by H-(auxiliary). As long as this confluence of roles may (and did!) lead to confusion in the literature, we propose an amended, three-Hilbert-space (3HS) reformulation of the same theory. As a byproduct of our analysis of the formalism we offer an amendment of the Dirac's bra-ket notation and we also show how its use clarifies the concept of covariance in time-dependent cases. Viaan elementary example we finally explain why in certain quantum systems the generator H-(gen) of the time-evolution of the wave functions may differ from their Hamiltonian H.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2009

Kód důvěrnosti údajů

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

Název periodika

Symmetry, Integrability and Geometry: Methods and Applications

ISSN

1815-0659

e-ISSN

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Svazek periodika

5

Číslo periodika v rámci svazku

-

Stát vydavatele periodika

UA - Ukrajina

Počet stran výsledku

19

Strana od-do

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Kód UT WoS článku

000267267900001

EID výsledku v databázi Scopus

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