1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Jun 25, 2012 #1
    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 [itex]\Delta H = \frac{m\omega^2 x^2}{2}[/itex] would not be considered time-dependent. Is the key that when you plug in the unperturbed solution for x, i.e., [itex]\frac{\alpha t}{m} + \beta[/itex], 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 [itex]\Delta H = \frac{\epsilon m^2 \omega_0^2 q^3}{q_0}[/itex], could also have been treated as a time-dependent problem.

    Any insight would be appreciated! Thanks!

    Dan
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted