Given a system,(adsbygoogle = window.adsbygoogle || []).push({});

[itex]H = H_0 + V[/itex]

V is a small perturbation that does not depend on time.

the system is in [itex]|E_0>[/itex] at time [itex]t_0[/itex]

[itex]H_0 |E_n> = E_n |E_n> [/itex]

[itex]H_0 |E_0> = E_0 |E_0> [/itex]

Let [tex]|\Psi(t)>[/tex] be the solution of the system.

Let [tex]|\Phi(t)>[/tex] be the solution of the system without perturbation.

Let [tex]|u(t)> = |\Psi(t)> - |\Phi(t)>[/tex].

Show that [tex]|<E_n|u(t)>|^2 = 4 |V_{n0}|^2 [{{\sin(t - t_0)(E_n - E_0)/\hbar}\over{E_n - E_0}}]^2[/tex]

at lowest order

No matter how many times I try, the answer I get is

[tex]|<E_n|u(t)>|^2 = 2 |V_{n0}|^2 [{{1 - \cos(t - t_0)(E_n - E_0)/\hbar}\over{E_n - E_0}}]^2[/tex]

Please help!!!

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

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!

# Homework Help: Time-dependent Perturbation

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