Strengthened PT-symmetry with P $\neq$ P$^\dagger$
| dc.creator | Znojil, Miloslav | |
| dc.date | 2006-01-09 | |
| dc.date.accessioned | 2026-07-07T07:00:18Z | |
| dc.date.available | 2026-07-07T07:00:18Z | |
| dc.description | Two alternative scenarios are shown possible in Quantum Mechanics working with non-Hermitian $PT-$symmetric form of observables. While, usually, people assume that $P$ is a self-adjoint indefinite metric in Hilbert space (and that their $P-$pseudo-Hermitian Hamiltonians $H$ possess the real spectra etc), we propose to relax the constraint $P=P^\dagger$ as redundant. Non-Hermitian triplet of coupled square wells is chosen for illustration purposes. Its solutions are constructed and the observed degeneracy of their spectrum is attributed to the characteristic nontrivial symmetry $S={P}^{-1} {P}^\dagger \neq I$ of the model $H$. Due to the solvability of the model the determination of the domain where the energies remain real is straightforward. A few remarks on the correct (albeit ambiguous) physical interpretation of the model are added. | |
| dc.description | 10 pp. + 1 figure | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0601048 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0601048 | |
| dc.identifier | Phys. Lett. A 353 (2006) 463 - 468 | |
| dc.identifier | doi:10.1016/j.physleta.2006.01.014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108000 | |
| dc.subject | Quantum Physics | |
| dc.title | Strengthened PT-symmetry with P $\neq$ P$^\dagger$ | |
| dc.type | text |