1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Average value in a one-dimensional well

  1. Mar 14, 2007 #1

    kreil

    User Avatar
    Gold Member

    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
    [tex]sin^2[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Average value in a one-dimensional well
Loading...