On the role of weak pseudo-Hermiticity in quasi-Hermitian models
نویسنده
چکیده
We list some reasons why among P−pseudo-Hermitian Hamiltonians H = P HP with real spectra, the “weakly pseudo-Hermitian” ones (i.e., those employing P 6 = P, even when belonging to the former class) form such an interesting special family that they deserve a special name and attention. In particular we show that for P 6 = P, the current auxiliary involutive operator of charge C gets complemented by another involutive “quasiparity” operator Q. We show how, in this language, the standard quantum mechanics can be restored via inner product 〈ψ1 | PQ |ψ2〉 = 〈ψ1 | CP |ψ2〉 in the Hilbert space of states. PACS 03.65.Ge; 03.65.Ca; 03.65.Ta e-mail: [email protected]
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