Explicit Form of Solution of Two Atoms Tavis-Cummings Model

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In this paper we consider the two atoms Tavis--Cummings model and give an explicit form to the solution of this model which will play a central role in quantum computation based on atoms of laser--cooled and trapped linearly in a cavity. We also present a problem of three atoms Tavis--Cummings model which is related to the construction of controlled--controlled NOT operation (gate) in quantum computation.
Latex file, 11 pages. After submitting the paper we received some comments, so we add Appendix to reply to one of them

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