# Time dependent pertubation theory

1. Oct 17, 2012

### 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 dont 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!

2. Oct 18, 2012

### Jano L.

The equation is a consequence of time-dependent Schrodinger 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?

3. Oct 19, 2012

### geoduck

I think intuitively Vnm 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.