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Radial part of wave function in respect to spherical harmonic

  1. Jan 7, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider a Wavefunction:
    [tex]\psi(x,y,z)=K(x+y+x^2-y^2)e^{-r/a}[/tex]
    Find expectation value of [tex] L^{2} , L_{z}^{2}, L_{x}^{2}[/tex].

    2. Relevant equations



    3. The attempt at a solution
    The first step would be a rewriting a wavefunction in terms of spherical coordinates:
    [tex]\psi=Kr(\cos\phi \sin \theta + 2 \sin \phi \cos \theta +r(\cos^{2} \phi \sin^{2} \theta - \sin^{2} \phi \sin^{2} \theta )) [/tex]

    My Question is : is it fair to skip the radial part and just forget about it. Normalize the Wavefunction for just the angular part , and then consider a mean values of Angular Momentum Operators ? Or should i normalize the wavefunction including r ? It bothers me because of the r squared in the equation.
     
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  3. Jan 8, 2012 #2

    vela

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    You can't neglect the radial functions.
     
  4. Jan 8, 2012 #3
    Just to make it clear - i need to do all next steps with the radial part ?
     
  5. Jan 8, 2012 #4

    vela

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    It depends what your next steps are. You eventually need to normalize the wave function, so you need to take into account the radial function somewhere along the way.

    By the way, you seem to have dropped the exponential factor when you rewrote the function in terms of spherical coordinates.
     
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