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Homework Help: Probability of finding a system an eigenstate

  1. Aug 31, 2014 #1
    1. The problem statement, all variables and given/known data

    As the homework problem is written exactly:
    Consider the quantum mechanical system with only two stationary states |1> and |2> and energies E0 and 3E0, respectively. At t=0, the system is in the ground state and a constant perturbation <1|V|2>=<2|V|1>=E0 is switched on. Calculate the probability of finding the system in the state |2>.

    2. Relevant equations
    H=V (I'm just assuming these states must be such that there is no kinetic energy and E=V, but that's just my guess - professor lacks communication skills at times).

    |c1|2 + |c2|2 = 1
    P(|2>)=|c2|2 (thus, I need c2 to solve the problem!)

    3. The attempt at a solution
    Well, I'm completely confused as to why he gave us <1|V|2>=<2|V|1>=E0, what that even means, and where I'm supposed to retrieve the probability coefficients which is all I need to solve the problem.
  2. jcsd
  3. Sep 1, 2014 #2


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    Hi there!

    Have you learned non degenerate perturbation theory? This is the formalism required to do this problem. What formula have you seen for perturbation theory?
  4. Sep 1, 2014 #3
    No, at least not that I know of. I'm familiar with chapters 1-4 in Griffiths, if that helps.
  5. Sep 1, 2014 #4


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    Also you are given the complete information about the unperturbed Hamiltonian!
  6. Sep 1, 2014 #5
    Right, I get that I have all of the matrix elements of the Hamiltonian, but I'm not sure how that's going to help me determine that probability of finding the system in state |2>. Also, we've never covered non degenerate perturbation theory, so is there another more elementary way to solve this problem?
  7. Sep 1, 2014 #6


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    No, this isn't right. You add V to the existing Hamiltonian, so H=H0+V. What are the matrix representations of H0, V, and H? You should be able to figure out the rest from there.

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