About: Three-Hilbert-Space Formulation of Quantum Mechanics

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. Via an 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. 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. Via an 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. (en)
Title	Three-Hilbert-Space Formulation of Quantum Mechanics Three-Hilbert-Space Formulation of Quantum Mechanics (en)
skos:prefLabel	Three-Hilbert-Space Formulation of Quantum Mechanics Three-Hilbert-Space Formulation of Quantum Mechanics (en)
skos:notation	RIV/61389005:_____/09:00329440!RIV10-MSM-61389005
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA202/07/1307), P(LC06002), Z(AV0Z10480505)
http://linked.open...iv/cisloPeriodika	-
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Znojil, Miloslav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav jaderné fyziky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	346304
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/09:00329440
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	formulation of Quantum Mechanics; cryptohermitian operators of observables; triplet of the representations of the Hilbert space of states (en)
http://linked.open.../riv/klicoveSlovo	cryptohermitian operators of observables formulation of Quantum Mechanics triplet of the representations of the Hilbert space of states
http://linked.open...odStatuVydavatele	UA - Ukrajina
http://linked.open...ontrolniKodProRIV	[C38752115971]
http://linked.open...i/riv/nazevZdroje	Symmetry, Integrability and Geometry: Methods and Applications
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Doppler Institute for Mathematical Physics and Applied Mathematics PT symmetry, supersymmetry and solvable models
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	5
http://linked.open...iv/tvurceVysledku	Znojil, Miloslav
http://linked.open...ain/vavai/riv/wos	000267267900001
http://linked.open...n/vavai/riv/zamer	Jaderná fyzika a příbuzné obory v základním, aplikovaném a interdisciplinárním výzkumu
issn	1815-0659
number of pages	19 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Three-Hilbert-Space Formulation of Quantum Mechanics Three-Hilbert-Space Formulation of Quantum Mechanics Three-Hilbert-Space Formulation of Quantum Mechanics Three-Hilbert-Space Formulation of Quantum Mechanics

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