Hi, I am wondering why the associated Laguerre Polynomial for the 3s hydrogen wave function is (27-18σ+2σ(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}).

My physical chemistry book tells me that the complete hydrogen wave function is given by:

[itex]\Psi[/itex](r,[itex]\theta[/itex],[itex]\phi[/itex])= R_{nl}Y[itex]^{m}_{l}[/itex]([itex]\theta[/itex],[itex]\phi[/itex])

and R_{nl}(r) uses the Laguerre polynomial L[itex]^{1}_{3}[/itex](x)=-3!(3-3x+(1/2)x^{2}).

How does this become (27-18σ+2σ^{2})? I understand that the σ = Zr/a_{0}, but how does the 27 and 2 come about? According to my calculations it should be (18-18σ+3σ^{2}).

Please help me!! I've been wracking my brain about this for way too long and cannot seem to find how this difference from the wave function given in my book and the wave function I produced using the complete hydrogen atomic wave function form comes about.

Thank you!!

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# 3s Hydrogen Wave Function

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