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Normalized Wave-Function

  1. Jun 4, 2012 #1
    1. The problem statement, all variables and given/known data
    Its simple, I've encountered this problem in Beiser's book and it doesn't seem right:

    Prove that the function [tex]R_{10}(r) = \frac{2}{a_{0}^{3/2}}\cdot e^{-\frac{r}{a_0}} [/tex] is normalized.


    2. Relevant equations
    [tex]\int_{-\infty}^{\infty} |\psi|^2 dV = 1 [/tex]



    3. The attempt at a solution
    I figured it's simply just taking the integral
    [tex]R_{10} (r)=\int^{\infty}_{0}( \frac{2}{a_{0}^{3/2}}\cdot e^{-\frac{r}{a_0}})^2dr = 1 [/tex]
    but the result is not 1, it's [tex]2/a_0^2[/tex]
     
  2. jcsd
  3. Jun 4, 2012 #2

    Simon Bridge

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    Don't you need r²dr instead of just dr?
    (volume integral, spherical-polar coords.)
     
  4. Jun 4, 2012 #3
    Yes it appears that solves the problem, thanks!
     
  5. Jun 4, 2012 #4
    I would enjoy a pointer as to where this comes from exactly, maybe a link?

    edit: just standard triple integration in 3 coordinates?
     
    Last edited: Jun 4, 2012
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