Consider a quantum system subject to an oscillating perturbation: where A need not be Hermitian. Show that for large t this perturbation leads to first-order transitions that may either absorb or emit...

Consider a quantum system subject to an oscillating perturbation:

where A need not be Hermitian. Show that for large t this perturbation leads to first-order transitions that may either absorb or emit an energy ω, and that the first-order rates for these are

This is sometimes used as a semi classical approach to analyzing the interaction of an atom with the electromagnetic field, in which the field is treated as an external classical perturbation to the (quantum) atom. A passing electromagnetic wave subjects the atom to an oscillating potential gradient, so that the atom may either absorb or emit an energy ω.