Three-Hilbert-Space Formulation of Quantum Mechanics

Result code in IS VaVaI

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Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Three-Hilbert-Space Formulation of Quantum Mechanics

Original language description

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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BE - Theoretical physics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2009

Confidentiality

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

Name of the periodical

Symmetry, Integrability and Geometry: Methods and Applications

ISSN

1815-0659

e-ISSN

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Volume of the periodical

5

Issue of the periodical within the volume

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Country of publishing house

UA - UKRAINE

Number of pages

19

Pages from-to

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UT code for WoS article

000267267900001

EID of the result in the Scopus database

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