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Physical Review A

Reply to “Comment on ‘Cyclic quantum-evolution dependence on the Hamiltonian and geometrical phase’ ”

Lian-Ao Wu

Published Sep 1, 1997• 0 citations
Publisher

Abstract

I reply to the Comment [A. Mostafazadeh, Phys. Rev. A 55, 4640 (1997)] on my paper in Phys. Rev. A 53, 2053 (1996). In particular, there is nothing in the Comment except the final paragraph, which points out my two sick sentences in English. I give a simple example to explain my original meaning of the two sick English sentences and try to correct them.

DOI
10.1103/physreva.56.2481

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I reply to the Comment [A. Mostafazadeh, Phys. Rev. A 55, 4640 (1997)] on my paper in Phys. Rev. A 53, 2053 (1996). In particular, there is nothing in the Comment except the final paragraph, which points out my two sick sentences in English. I give a simple example to explain my original meaning of the two sick English sentences and try to correct them.
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 \textbf{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.
The preceding Comment challenged my claim that potentials might be just auxiliary mathematical tools and that they are not necessary for explaining physical phenomena. The Comment did not confront my explanation without the potentials of the Aharonov-Bohm effects that appeared in the original article, but stated that I cannot apply this explanation for seven other examples. In my reply, using my method, I provide explanations of one of the examples, show that two other examples are not relevant, and agree that the remaining examples require further analysis. However, I argue that none of the examples provides robust counterexamples to my claim, similar to the original Aharonov-Bohm setups which were explained in my article, so the Comment does not refute my claim.