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Sakurai ch 2 problem 14.b

  1. Sep 7, 2007 #1

    malawi_glenn

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    1. The problem statement, all variables and given/known data

    Consider a one-dim harm osc; start with the Schrödinger equation (SE) for the state vector, then derive the SE for the momentum-space wave function.


    3. The attempt at a solution

    My answer is this, all primed letters are numbers (as in sakurai notation). Its gonna take a while for me to do all my steps, so before I do all that; I just want to see if someone here can confirm my answer as the right one (sakurai is a popular book to teach from). If it is now the correct answer, I will post all the steps I've done so you guys can put me in right direction. Thanx in advance physics fellows!

    [tex] \left(\dfrac{(p')^2}{2m} - \dfrac{\hbar ^2 \omega ^2 m }{2} \dfrac{\partial^{2}}{(\partial p')^2} \right) \psi _{\alpha}(p') = i \hbar \dfrac{\partial}{\partial t}\psi _{\alpha}(p') [/tex]

    I have found many answers to sakurai on the web, but not to this one; and our teacher said that this was a good problem to do.
     
  2. jcsd
  3. Sep 7, 2007 #2

    cristo

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    That looks correct to me.
     
  4. Sep 7, 2007 #3

    malawi_glenn

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    Thanx alot for your answer!
     
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