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In this letter the explicit form of evolution operator of the Tavis-Cummingsmodel with three and four atoms is given. This is an important progress inquantum optics or mathematical physics.Comment: Latex file, 10 pages. We combined quant-ph/0404034(the three atoms  case) and quant-ph/0406184(the four atoms case) into an article. to appear in  International Journal of Geometric Methods in Modern Physic

EXPLICIT FORM OF THE EVOLUTION OPERATOR OF TAVIS–CUMMINGS MODEL: THREE AND FOUR ATOMS CASES