Three-Hilbert-Space Formulation of Quantum Mechanics
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Three-Hilbert-Space Formulation of Quantum Mechanics
|
|
| Creator |
Znojil, M.
|
|
| 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.
|
|
| Date |
2019-02-19T19:46:57Z
2019-02-19T19:46:57Z 2009 |
|
| Type |
Article
|
|
| Identifier |
Three-Hilbert-Space Formulation of Quantum Mechanics / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 25 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 81Q10; 47B50 http://dspace.nbuv.gov.ua/handle/123456789/149281 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|