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Three-Hilbert-Space Formulation of Quantum Mechanics

SYSNO ASEP	0329440
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Three-Hilbert-Space Formulation of Quantum Mechanics
Author(s)	Znojil, Miloslav (UJF-V)_{RID, ORCID, SAI}
Source Title	Symmetry, Integrability and Geometry: Methods and Applications. - : Natsional'na Akademiya Nauk Ukrainy - ISSN 1815-0659 Roč. 5, - (2009), 001/1-001/19
Number of pages	19 s.
Action	7th Workshop on Quantum Physics with Non-Hermitian Operators
Event date	29.06.2007-11.07.2007
VEvent location	Benasque
Country	ES - Spain
Event type	WRD
Language	eng - English
Country	UA - Ukraine
Keywords	formulation of Quantum Mechanics ; cryptohermitian operators of observables ; triplet of the representations of the Hilbert space of states
Subject RIV	BE - Theoretical Physics
R&D Projects	GA202/07/1307 GA ČR - Czech Science Foundation (CSF)
	LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS)
CEZ	AV0Z10480505 - UJF-V (2005-2011)
UT WOS	000267267900001
DOI	10.3842/SIGMA.2009.001
Annotation	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.
Workplace	Nuclear Physics Institute
Contact	Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228
Year of Publishing	2010

Number of the records: 1