(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Normalization of radial Laguerre-Gauss

Normalize [tex] \Psi _n (r) = h_n L_n (2\pi r^2) e^{-\pi r^2} [/tex]

2. Relevant equations

[tex]\int _0 ^{\infty} e^{-x} \, x^k \, L_n ^{(k)} (x) \, L_m ^{(k)} (x) dx = \frac{(n+k)!}{n!} \delta _{m,n} [/tex]

3. The attempt at a solution

[tex]1 = \int _0 ^{\infty} \Psi _m ^{\ast} (r) \Psi _n (r) dr = \int _0 ^{\infty} h_m ^{\ast} L_m (2\pi r^2) e^{-\pi r^2} h_n L_n (2\pi r^2) e^{-\pi r^2} dr [/tex]

If I let [itex] x = 2\pi r^2[/itex], then I get [itex] dx = (4\pi r) dr[/itex]. The radial dependence bothers me. I think there's a step I'm missing out.

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# Homework Help: Normalization of radial Laguerre-Gauss

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