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Using perturbation to calculate first order correction
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[QUOTE="Leechie, post: 5718417, member: 609087"] Thanks for your help John. I don't think its missing the factor 4##\pi##. The original state is given as ##\psi_{1,0,0} = R_{nl} \left( r \right) Y_{lm}\left( \theta, \phi \right) ##, and I made it that the spherical harmonics are normalized in the state: ##Y_{0,0}\left( \theta, \phi \right) = \frac 1 {\sqrt {4 \pi}}##. Ah, I can see it now, the missing factor 2 and I've forgotten to change the exponents back after substitution. Thanks for pointing those out. I confident the perturbation is correct and the question I've been given involves calculating the first-order correction for a modified Coulomb model of a hydrogen atom where ##V\left(r\right)=- \frac {e^2b^2} {4 \pi \varepsilon_0 r^2} ## where ## 0 \lt r \leq b ## and ##V\left(r\right)=- \frac {e^2} {4 \pi \varepsilon_0 r} ## where ## r \gt b##. So I think I have to integral from ##0## to ##b##. I'm quite new to this forum and I'm really amazed at how helpful and friendly everyone is here. I don't know where I'd be without PF! [/QUOTE]
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Using perturbation to calculate first order correction
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