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Homework Help: Show that the wavefunction is normalized

  1. Mar 10, 2013 #1
    Problem:

    Show that

    [itex]\Theta_{20}=\frac{\sqrt{10}}{4}(3cos^{2}\theta-1)[/itex]

    is a normalized solution to

    [itex]\frac{1}{sin\theta}\frac{d}{d\theta}(sin\theta \frac{d\Theta}{d\theta})+[l(l+1)-\frac{m_{l}^{2}}{sin^{2}\theta}]\Theta=0[/itex]

    Solution:

    I know how to show it's a solution, but I'm stuck on showing it's normalized.

    I know that in general, a normalized wavefunction obeys,

    [itex]\int^∞_{-∞}\mid \psi \mid^{2}dV=1[/itex]

    So would this particular normalized angular wavefunction obey the following?

    [itex]\int^{\pi}_0\mid \Theta_{20}(\theta) \mid^{2}\sin\theta d\theta=1[/itex]

    I'm sorry if this is very elementary, but we just started doing this type of thing in my modern physics class. We haven't used any complex methods to solve these, so I don't think this problem will involve any advanced operators or anything of that sort. Any suggestions?

    I just need help setting the integral up.
     
    Last edited: Mar 10, 2013
  2. jcsd
  3. Mar 11, 2013 #2

    DrClaude

    User Avatar

    Staff: Mentor

    Exactly.
     
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