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On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models
Репозиторій DSpace/Manakin
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4, випуск за цей рік
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On the Role of the Normalization Factors κn and of the Pseudo-Metric P ≠ P† in Crypto-Hermitian Quantum Models
Інший ID:
2000 Mathematics Subject Classification: 81Q10; 47B50
Посилання:
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.
Підтримка:
This paper is a contribution to the Proceedings of the 3-rd Microconference “Analytic and Algebraic Methods III”. Work supported by GACR, grant Nr. 202/07/1307, Institutional Research Plan AV0Z10480505 and by the MSMT “Doppler Institute” project Nr. LC06002.
Дата:
2008
Переглядів:
501
Завантажень:
201
Анотація:
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>.
