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A finite number of harmonic oscillators coupled to infinitely manyenvironment oscillators is fundamental to the problem of understanding quantumdissipation of a small system immersed in a large environment. Exact operatorsolution as a function of time is given to this problem, by using diagonalizeddynamical variable of the entire system, the small system plus the environment.The decay law of prepared initial configuration is worked out in greatestdetail. A clear separation of the exponential- and the power-law decay periodis made possible by our method. Behavior of physical quantities atasymptotically late times can be understood in terms of the overlap probabilityof the system variable with the diagonal variable of the entire system.Comment: 15 pages, LATEX file with 2 PS figures.Figures also available at  ftp://tuhep.phys.tohoku.ac.jp/preprints/operato

Quantum Dissipation in Open Harmonic Systems: --Operator Solution and Application to Decay Process--