ABSTRACT
This chapter presents the study of perturbation methods for the solution to the Schrodinger equation and focuses on to the case where the perturber depends explicitly on time. Just as in the case of the time-independent perturbation theory, the corrections to the eigenvalues and eigenvectors of a system described by a time-dependent Hamiltonian are found. In the non-stationary case, in which the Hamiltonian of the system depends on time, one can find the time evolution of the state vector by solving the time-dependent Schrodinger equation. The iterative solution involves the total Hamiltonian of the system. It may result in complicated expressions to evaluate. The splitting of the total Hamiltonian into stationary and time- dependent parts allows to work in the interaction picture. The chapter illustrates Fermi Golden Rule, which shows that in an atom composed of a large number of energy states, the probability of a transition is proportional to time.
