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ISW hamiltonian in energy basis

  1. Nov 20, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the matrix elements of the Hamiltonian in the energy basis for the ISW. Is it
    diagonal? Do you expect it to be diagonal?

    2. Relevant equations

    [itex] H=\frac{p^2}{2m}+V [/itex]

    [itex] \frac{d}{dt}\langle Q \rangle = \frac{i}{\hbar} \langle[\hat H, \hat Q] \rangle + \langle \frac{\partial \hat Q}{\partial t} \rangle [/itex]

    3. The attempt at a solution

    How should I convert H into matrix?
  2. jcsd
  3. Nov 27, 2011 #2
    I assume by ISW you mean "infinite square well". Anyway, you're not asked to convert H into a matrix. You are asked to find its matrix elements. Some things: 1) Matrix elements are indexed scalars. 2) "Matrix elements" carries the connotation of "eigenvalues". 3) What happens when the Hamiltonian operator "hits" an energy-basis vector/ket? 4) What is the dual of this equation? Does that get the gears working?
  4. May 14, 2012 #3
    Thanks bjnartown, I searched and found this. I already had the correct math down, but your explanation is wonderful and I really learned a lot from it. I seriously created an account to tell you that, lol.
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