Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have a problem with the very nature of time dependant perturbation theory (TDPT). In TDPT, we consider a system of Hamiltonian H(t) = H_0 (for t<0), H(t)=H_0 + kW(t) (for t>0) [where k<<1], where H_0 is, for simplicity, discrete, non-degenerate and time-independent, and given that at t=0, the state of the system is |phi_i> (an eigenstate of H_0), we are interested in calculating P_if(t), the probability of finding the system in another eigenstate of H_0, |phi_f>, at time t.

But this does not make sense because at t, the hamiltonian is no longer H_0, so it will, in general, not have |phi_f> as an eigenstates. But we know that the result of a measurement will project the wave-function into one of the eigenfunction. So as soon as |phi_f> is not an eigenstate of H(t), the probability of finding the system in |phi_f> will be 0.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Time dependant perturbation

**Physics Forums | Science Articles, Homework Help, Discussion**