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Potential and Kinetic energy commutator

  1. Nov 9, 2014 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution

    I think my problem is with executing the chain rule on the first term:


    The x2ψ'' terms cancel out but I'm left with the +4xψ' term which I makes me suspect that I've made a mistake somewhere.
  2. jcsd
  3. Nov 9, 2014 #2


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    It's actually the product rule, not the chain rule. Your calculation is okay except for a few minor errors. (Where'd the k go?)

    Neglecting the constant factors out front, you ended up with ##(2x\frac{\partial}{\partial x} + 1)\psi##. You can show this equals ##(x\frac{\partial}{\partial x} + \frac{\partial}{\partial x} x)\psi##, which probably looks more correct to you.
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