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Homework Help: Average value in a one-dimensional well

  1. Mar 14, 2007 #1


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    1. The problem statement, all variables and given/known data
    Show that the average value of x2 in the one-dimensional well is

    [tex](x^2)_{av}=L^2(\frac{1}{3}-\frac{1}{2n^2 \pi^2})[/tex]

    2. Relevant equations

    wave fuction in 1-dim well:
    [tex]\psi_n(x)=\sqrt{\frac{2}{L}}sin(\frac{n \pi x}{L})[/tex]

    [tex]x^2_{av}=\int_{0}^{L}|\psi(x)|^2 x^2 dx[/tex]

    3. The attempt at a solution

    Im having trouble evaluating the integral:

    [tex]x^2_{av}=\frac{2}{L} \int_0^Lsin^2(\frac{n \pi x}{L})x^2dx[/tex]

    i think this needs to be integrated by parts, but could it be in a table somewhere?
    Last edited: Mar 14, 2007
  2. jcsd
  3. Mar 14, 2007 #2
    There should be a table, when I took Quantum mechanics, usually the professor gave a table with solution of some integral(like this one for example), even in exams he did that.
    But try to do it manually, more experience..
  4. Mar 15, 2007 #3
    yah, simplest way to solve it is integration by parts.
    dont forget to use double angles to get rid of
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