1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: 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

    User Avatar
    Science Advisor
    Homework Helper

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook