dorsal/arxiv
View SchemaStrengthened PT-symmetry with P $\neq$ P$^\dagger$
| Authors | Miloslav Znojil |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0601048 |
| URL | https://arxiv.org/abs/quant-ph/0601048 |
| DOI | 10.1016/j.physleta.2006.01.014 |
| Journal | Phys. Lett. A 353 (2006) 463 - 468 |
Abstract
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.
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"abstract": "Two alternative scenarios are shown possible in Quantum Mechanics working\nwith non-Hermitian $PT-$symmetric form of observables. While, usually, people\nassume that $P$ is a self-adjoint indefinite metric in Hilbert space (and that\ntheir $P-$pseudo-Hermitian Hamiltonians $H$ possess the real spectra etc), we\npropose to relax the constraint $P=P^\\dagger$ as redundant. Non-Hermitian\ntriplet of coupled square wells is chosen for illustration purposes. Its\nsolutions are constructed and the observed degeneracy of their spectrum is\nattributed to the characteristic nontrivial symmetry $S={P}^{-1} {P}^\\dagger\n\\neq I$ of the model $H$. Due to the solvability of the model the determination\nof the domain where the energies remain real is straightforward. A few remarks\non the correct (albeit ambiguous) physical interpretation of the model are\nadded.",
"arxiv_id": "quant-ph/0601048",
"authors": [
"Miloslav Znojil"
],
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"quant-ph"
],
"doi": "10.1016/j.physleta.2006.01.014",
"journal_ref": "Phys. Lett. A 353 (2006) 463 - 468",
"title": "Strengthened PT-symmetry with P $\\neq$ P$^\\dagger$",
"url": "https://arxiv.org/abs/quant-ph/0601048"
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