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Summary form only given.C.K Law et al. (1995) directed attention to the interaction between a field inside a cavity with a movable boundary and an atom inside the cavity and calculated the effect of the oscillatory motion of a boundary on the spontaneous spectrum in the adiabatic regime. In the present paper we show that fascinating features of such an interaction appear even in the case where the adiabatic approximation is satisfied. The dynamics of a three-state atom interacting with a cavity field is considered. Two states out of the three do not couple with each other directly but via the cavity modes, whose eigenfrequencies determined by the cavity length change with time. It is shown that the transition in the cavity can be enhanced through the indirect coupling. In the present analysis, the formulation based on the mode expansion of the cavity field is used. Since the mode functions contain a cavity length explicitly, the moving-boundary condition is taken into account in the population dynamics. This formulation also allows us to calculate the position-dependent behavior of the system. Here the discussion is restricted to the case where the atom exists at the center of the cavity. Initially the atom is assumed to be prepared in its first excited state. Coupling between the two states is enhanced under some conditions and it results in a population inversion between the two excited states. Furthermore, an interaction between two two-state atoms located in a cavity is studied and the dependence of the energy shift and interatomic energy transfer on the cavity length are analyzed. We found a resonance effect in the cavity length-dependent transition dipole.