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Homework Help: ND Pertubation theory: Second order correction

  1. Jun 2, 2016 #1
    1. The problem statement, all variables and given/known data
    Calculate the second-order correction to the ground-state energy of the stationary states of the system.

    The perturbed Hamiltonian is:

    H' =- (/gamma /hbar m /omega)/2 (a+ - a-) ^2

    2 & 3. Relevant equatio and the attempt at a solution
    QM d.PNG
    This is not right. I follow the same procedure as letting the ladder operators act on eigenvalues, i.e. that a+|n> becomes (√(n+1))|n+1>
    Last edited: Jun 2, 2016
  2. jcsd
  3. Jun 2, 2016 #2


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    Did you have a question?
  4. Jun 2, 2016 #3
    I didn't notice at first that my post is lacking some details.

    My question is this: Where in my calculations did I make a mistake in calculating a solution to the problem?
  5. Jun 3, 2016 #4


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    Why do you have factors of "n" all over the place? There should be only an "m" and in each term is has a specific value (like m=2!) so you should get numbers for all the matrix elements (and most of them are zero)
  6. Jun 4, 2016 #5
    How do I figure out which value of m each matrix element should have?
  7. Jun 4, 2016 #6
    I figured it out.

    I got the following result: sqrt(1)sqrt(2).

    (Which is correct)
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