(739) |

where does not contain time explicitly, and is a small time-dependent perturbation. It is assumed that we are able to calculate the eigenkets of the unperturbed Hamiltonian:

(740) |

We know that if the system is in one of the eigenstates of then, in the absence of the external perturbation, it remains in this state for ever. However, the presence of a small time-dependent perturbation can, in principle, give rise to a finite probability that a system initially in some eigenstate of the unperturbed Hamiltonian is found in some other eigenstate at a subsequent time (because is no longer an exact eigenstate of the total Hamiltonian). In other words, a time-dependent perturbation allows the system to make transitions between its unperturbed energy eigenstates. Let us investigate such transitions.

Richard Fitzpatrick 2013-04-08