Reply to Comment on “Time-dependent quasi-Hermitian Hamiltonians and the unitary quantum evolution”

In his fresh “Comment” (arXiv:0711.0137v1), A. Mostafazadeh reacts on my very recent letter (arXiv:0710.5653v1) where I tried to clarify certain misunderstandings which occurred in A. M., Phys. Lett. B 650, 208 (2007) [arXiv:0706.1872v2, “Paper”]. As long as the “Comment” offers a new support of the original assertions made in the “Paper”, I feel obliged to re-clarify the matter by extending my argumentation. I insist that it is possible to escape the main conclusion of the “Paper”, indeed. In particular, I point out a gap in the new calculations in “Comment”, add a few remarks on the notation and reconfirm that the unitarity of the time-evolution DOES NOT require the time-independence of the metric operator. PACS number: 03.65.Ca, 11.30.Er, 03.65.Pm, 11.80.Cr In the notation used in my preprint [1] as well as in the A. Mostafazadeh’s brand new comment on it [2], the symbol Θ denotes a (positive) metric operator with a square root ω := √ Θ, both assigned to a possibly time-dependent Θ-pseudo-Hermitian Hamiltonian operator H acting on a reference Hilbert space H with the inner product 〈·|·〉. Moreover, • symbol h := ωHω is chosen to denote the equivalent Hermitian Hamiltonian leading to the evolution operator u such that i~∂tu(t) = h(t)u(t) and u(0) = I, where I stands for the identity operator, ∗e-mail: [email protected]