Time dependent pertubation theory

[Kontilera]

Okey, so I´m taking a course in QM and I feel that I got a grip of most of it.
But then we arrive at this formulea $$i\hbar\frac{\partial}{\partial t} c_n(t) = \sum_m \hat{V}_{nm} e^{i\omega_{nm} t}c_m(t),$$ where $$\omega_{nm} \equiv \frac{(E_n - E_m)}{\hbar}.$$
In other words time dependent pertubation theory. And I just feel confused. I don't know how to start tackle it with my intuition.

What are, in your opinion, the first intuitional things I should remark when it comes to this equation? What does it tell about my physics without having to do some big derivations?

Thanks!

 

[Jano L.]

The equation is a consequence of time-dependent Schrödinger equation. It is a rule that the expansion coefficients c_n obey. This equation can be used to find approximate values of c's, and afterwards these can be used to find average values of physical quantities.
Does this help?

 

[geoduck]

I think intuitively V_nm represents scattering channels, a coupling of an m state to an n state in the interaction picture. The bigger the V, the bigger the coupling.

The fact that V _nm depends on time is not that important.