Floquet Theory of Multiphoton Transitions

In Chapter 6 we saw how the Floquet Hamiltonian for multiphoton processes arises from the semiclassical resolvent theory and how this Hamiltonian was found to be essentially equivalent to the projection of the quantum Hamiltonian onto the space of the occupation numbers. The fundamental property of the system that permits such a development is the periodicity of the semiclassical Hamiltonian in time and/or the periodicity of the stationary Hamiltonian in energy. In this chapter the Floquet theory of multiphoton transition amplitudes is developed in both the energy and time domains. We begin the energy-domain analysis with the construction of a general Floquet Hamiltonian applicable to an N-electron system and to multipolar interactions.