Počet záznamů: 1

Three-Hilbert-Space Formulation of Quantum Mechanics

  1. 1.
    0329440 - UJF-V 2010 RIV UA eng J - Článek v odborném periodiku
    Znojil, Miloslav
    Three-Hilbert-Space Formulation of Quantum Mechanics.
    Symmetry, Integrability and Geometry: Methods and Applications. Roč. 5, - (2009), 001/1-001/19 ISSN 1815-0659.
    [7th Workshop on Quantum Physics with Non-Hermitian Operators. Benasque, 29.06.2007-11.07.2007]
    Grant CEP: GA ČR GA202/07/1307; GA MŠk LC06002
    Výzkumný záměr: CEZ:AV0Z10480505
    Klíčová slova: formulation of Quantum Mechanics * cryptohermitian operators of observables * triplet of the representations of the Hilbert space of states
    Kód oboru RIV: BE - Teoretická fyzika
    Impakt faktor: 0.789, rok: 2009

    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.
    Trvalý link: http://hdl.handle.net/11104/0175477