Lie-algebraic approach to the calculation of quasi-energies

Perturbation theory for the calculation of quasi-energies on the basis of the Lie-algebraic approach

“…It is well known that, if only one of the two exponentials in the cosine function is retained in the interaction (rotating-field approximation), equation (7) with the Hamiltonian (13) can be solved exactly. The purpose of this example is to present the method and some results obtained in an attempt to find the quasi-energies and quasi-stationary states without the rotating-field approximation.…”

“…The system of equations ( 9) is solvable exactly in only a small number of elementary cases, one of which is considered in detail in our previous work [7]. As mentioned above, in most practically important problems, this system is not solvable exactly, and to find its solutions it is necessary to use approximate methods.…”