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Normalisation of associated Laguerre polynomials

  1. Nov 7, 2008 #1
    I'm looking right now at what purports to be the normalisation condition for the associated Laguerre polynomials:

    [tex]\int_0^\infty e^{-x}x^k L_n^k(x)L_m^k(x)dx=\frac{(n+k)!}{n!}\delta_{mn}[/tex]

    However, in the context of Schroedinger's equation in spherical coordinates, I find that my normalisation integral has a different form:

    [tex]|N|^2\int_0^\infty (\alpha r)^l e^{-\alpha r}[L_{n-l-1}^{2l+1}(\alpha r)]^2 r^2 dr=1[/tex]

    I understand that I can evaluate this integral using the generating function of the associated Laguerre polynomials, but I'm a bit confused about why there are two forms for normalisation. Can anyone shed any light on this? Thanks.
  2. jcsd
  3. Dec 8, 2008 #2
    hey still need help on that?
  4. Dec 8, 2008 #3
    No thanks I figured it out.
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