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!

Homework Help: Two State System Described by a Time-Dependent Hamiltonian

  1. Oct 23, 2013 #1
    1. The problem statement, all variables and given/known data
    A two state system is described the time dependent Hamiltonian
    [tex]\hat{H}=|\psi\rangle E\langle\psi|+|\phi\rangle E \langle\phi|+|\psi\rangle V(t)\langle\phi|+|\phi\rangle V(t)\langle\psi|[/tex]
    [tex]\langle \psi|\psi \rangle = 1=\langle \phi|\phi\rangle, \langle \phi|\psi \rangle=0=\langle \psi|\phi \rangle
    \\V(t)→0, t→±∞[/tex]
    Given that as t→-∞ the system was in the state $$|\psi\rangle$$ find the probability that it will end up in state $$|\phi\rangle$$ as t→+∞.

    2. Relevant equations
    $$\hat{H}_\psi|\psi\rangle = E|\psi\rangle$$
    $$\hat{H}_\phi|\phi\rangle = E|\phi\rangle$$
    $$\hat{H}_0= \hat{H}_\psi+\hat{H}_\phi$$

    3. The attempt at a solution
    To be completely honest, I don't even really know were to begin. I can somewhat grasp the fact that this time dependent Hamiltonian can be written as the sum of the time independent Hamiltonian and some perturbation V(t), but beyond that, I'm at a loss.
    Last edited: Oct 23, 2013
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

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