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: 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


    User Avatar
    Science Advisor
    Homework Helper

    The factorial of 0 is 1. :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook