On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models

Among P-pseudo-Hermitian Hamiltonians H = P⁻¹H†P with real spectra, the ''weakly pseudo-Hermitian'' ones (i.e., those employing non-self-adjoint P ≠ P†) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P ≠...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2008
1. Verfasser: Znojil, M.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2008
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/148972
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 25 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung:Among P-pseudo-Hermitian Hamiltonians H = P⁻¹H†P with real spectra, the ''weakly pseudo-Hermitian'' ones (i.e., those employing non-self-adjoint P ≠ P†) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P ≠ P†, the current involutive operator of charge C gets complemented by a nonequivalent alternative involutive quasiparity operator Q. We show how, in this language, the standard quantum mechanics is restored via the two alternative inner products in the physical Hilbert space of states, with <ψ₁|PQ|ψ₂> = <ψ1|CP|ψ2>.
ISSN:1815-0659