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Question in variational method (QM)

  1. Sep 10, 2015 #1
    1. The problem statement, all variables and given/known data

    Hi, in this book " [Nouredine_Zettili]_Quantum_Mechanics_Concepts ", Eq. (9.133)

    2. Relevant equations

    I don't know how the second line

    upload_2015-9-11_1-25-15.png

    had come from the first line:


    upload_2015-9-11_0-42-50.png


    3. The attempt at a solution


    I got only two terms such that:

    $$ < \psi_0| H | \psi_0 > = A^2 \int^{+\infty}_{-\infty} \Big( - \frac{2\alpha^2 h^2}{m} e^{-2\alpha x^2} + \frac{1}{2} m \omega^2 x^2 e^{-2\alpha x^2} \Big) dx $$


    So what I missed ?
     

    Attached Files:

    Last edited: Sep 10, 2015
  2. jcsd
  3. Sep 10, 2015 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I fixed the images in your post.

    The first derivative of ##e^{-\alpha x^2}## gives ##-2\alpha x e^{-\alpha x^2}##, the second derivative leads to ##(-2\alpha + 4\alpha^2 x^2) e^{-\alpha x^2}## and the second summand should give the missing term.
     
  4. Sep 10, 2015 #3
    Yap ..
     
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