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We present a new complete set of states for a class of open quantum systems,to be used in expansion of the Green's function and the time-evolutionoperator. A remarkable feature of the complete set is that it observestime-reversal symmetry in the sense that it contains decaying states (resonantstates) and growing states (anti-resonant states) parallelly. We can therebypinpoint the occurrence of the breaking of time-reversal symmetry at the choiceof whether we solve Schroedinger equation as an initial-condition problem or aterminal-condition problem. Another feature of the complete set is that in thesubspace of the central scattering area of the system, it consists ofcontributions of all states with point spectra but does not contain anybackground integrals. In computing the time evolution, we can clearly seecontribution of which point spectrum produces which time dependence. In thewhole infinite state space, the complete set does contain an integral but it isover unperturbed eigenstates of the environmental area of the system and hencecan be calculated analytically. We demonstrate the usefulness of the completeset by computing explicitly the survival probability and the escapingprobability as well as the dynamics of wave packets. The origin of each term ofmatrix elements is clear in our formulation, particularly the exponentialdecays due to the resonance poles.

Time-reversal symmetric resolution of unity without background integrals in open quantum systems