Time-Independent Rayleigh-Schrodinger Perturbation Theory

Since in the Floquet representation the Hamiltonian K defined on the enlarged Hilbert space is time-independent, the analysis of the effect of perturbations (like, e.g., transition probabilities) can be done by stationary perturbation theory, instead of the usual time-dependent one. Here we will present a formulation of stationary perturbation theory based on the iteration of unitary transformations (called contact transformations or KAM transformations) constructed such that the form of the Hamiltonian gets simplified. It is referred to as the KAM technique. The results are not very different from the ones of Rayleigh-Schrodinger perturbation theory, but conceptually and in terms of speed of convergence they have some advantages. 

Chapter 12 Time-Independent Rayleigh-Schrodinger Perturbation Theory... 

Some general remarks on the perturbation theory and the many-body approach are now in order. Let us review first the essence of the nondegenerate Rayleigh-Schrodinger perturbation theory. Consider the time-independent Schrodinger equation for the ground state ... 

In this section, we shall follow the main features of the derivation of the time-independent many-body Rayleigh-Schrodinger perturbation theory (mb-rspt) given by Paldus and Cfzek in their well-known review, published in 1975 [29]. 

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