Transition amplitudes corresponding to bound-bound multiphoton transitions with the emission or absorption of one and two Raman photons in the hydrogen atom have been evaluated following a recent method of Reiss. Results show that the transition probability varies smoothly for low values of
N, where
N is the number of intense photons absorbed or emitted during the transition. For larger values of
N the amplitude, however, has oscillatory behavior. A particular feature of the present method of calculation is that we find the "reduced" transition amplitude for induced emission of two Raman photons is enhanced compared with single-Raman-photon emission. Another distinctive feature is the appearance of many more extrema in the transition amplitude for higher transitions for multiphoton processes at high intensity.