Time-Dependent Perturbation Theory

InPerturbation theorytime-dependent this chapter, we deal with the quantum transitions between stationary states of a system subjected to a perturbation for a time lapse. The stationary states are described by the time-independent Hamiltonian \(\mathbf{H_0}\) and the perturbation by the time-dependent interaction \(\textbf{V}(t)\) . Except for a few cases, the Schrödinger equation with the full Hamiltonian \({\textbf{H}(t) = \textbf{H}_0 + \textbf{V}(t)}\) cannot be solved exactly. Approximate solutions are based on the expansion of the time evolution operator \(\textbf{U}(t,t_0)\) in series of \(\textbf{V}(t)\) powers. A concern of the perturbation methods is to make sure of the convergence of the perturbative expansion, that is mainly entrusted to the strength of the interaction. The lowest perturbation order provides accurate predictions for sufficiently weak interactions such as the Coulomb force, whereas more elaborated methods are requested by strong interactions like the nuclear force.