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Spherical Harmonics

  1. Nov 13, 2005 #1
    In solving the 3D hydrogen atom, we obtain a spherical harmonic, Y such that,
    [tex] Y_{lm}(\theta,\phi) = \epsilon\sqrt{\frac{(2l+1)}{(4\pi)}}\sqrt{\frac{(l-|m|)!}{(l+|m|)!}}e^{im\phi}P^m_l(cos \theta)[/tex]
    where [tex]\epsilon = (-1)^m [/tex] for [tex] m \geq 0 [/tex] and [tex] \epsilon = 1 [/tex] for [tex] m \leq 0 [/tex].
    In quantum, m = -l, -l+1, ..., l-1, l.
    But according to the formula above, when m = l, we should have zero and not a finite value, since [tex] l - |m| = 0 [/tex]. Which means the wavefunction should be zero when m = l.
    Where did I go wrong?
    Last edited: Nov 13, 2005
  2. jcsd
  3. Nov 13, 2005 #2


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    The factorial of 0 is 1. :)
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