# Classical Perturbation Theory-Time Dep. vs. Time Indep (Goldstein).

1. Jun 25, 2012

### Bosh

Classical Perturbation Theory--Time Dep. vs. Time Indep (Goldstein).

Hi,

I'm going through Goldstein, and I'm a little confused on the distinction between time dependent and time independent perturbation theory. In section 12.2, they do the case of a simple harmonic perturbation on force free motion. I would have thought that the perturbation $\Delta H = \frac{m\omega^2 x^2}{2}$ would not be considered time-dependent. Is the key that when you plug in the unperturbed solution for x, i.e., $\frac{\alpha t}{m} + \beta$, the perturbation hamiltonian is now time-dependent?

If so, it would seem that the example they treat in the section on time-independent perturbation theory, the anharmonic oscillator with $\Delta H = \frac{\epsilon m^2 \omega_0^2 q^3}{q_0}$, could also have been treated as a time-dependent problem.

Any insight would be appreciated! Thanks!

Dan