In this article, taking the exciton and polar-phonon interaction as an example, we introduce an integral operator to deal with the dynamical problem of exciton-phonon interaction. Compared with the methods of earlier arthors, our method has some characteristics : besides the binding energies which agree with the measured data of experiments, the lifetime of excitons, the renormalization factors of translational masses, and the relation between these quantities and temperature, are obtained simultaneously. This method may be used not only for the Is state, but also the states higher than Is state. Furthermore, this method may be extended to the anisotropic case and the case of degenerate valence band conveniently.
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