Three-Hilbert-Space Formulation of Quantum Mechanics
| dc.creator | Znojil, Miloslav | |
| dc.date | 2009-01-06 | |
| dc.date.accessioned | 2026-07-07T12:24:55Z | |
| dc.date.available | 2026-07-07T12:24:55Z | |
| dc.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 ${\cal H}^{\rm (auxiliary)}$ and ${\cal H}^{\rm (standard)}$) we spot a weak point of the 2HS formalism which lies in the double role played by ${\cal H}^{\rm (auxiliary)}$. 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 $H_{\rm (gen)}$ of the time-evolution of the wave functions may differ from their Hamiltonian $H$. | |
| dc.identifier | https://arxiv.org/abs/0901.0700 | |
| dc.identifier | http://arxiv.org/abs/0901.0700 | |
| dc.identifier | SIGMA 5 (2009), 001, 19 pages | |
| dc.identifier | doi:10.3842/SIGMA.2009.001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214472 | |
| dc.subject | Quantum Physics | |
| dc.subject | Mathematical Physics | |
| dc.title | Three-Hilbert-Space Formulation of Quantum Mechanics | |
| dc.type | text |