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I'm trying to solve the Schrodinger equation in cylindrical coordinates, is an hypothetical system using $V=\frac{d}{\rho}$ but I get this equation:

$$ \frac{d^2R}{d\rho^2}+\frac{1}{\rho}\frac{dR}{d\rho}+\left(\frac{d}{\rho}+k^2-\frac{m^2}{\rho^2}\right)R=0 $$

Where R is a fuction of $\rho$ and d, m and k are constant.This just the radial part

This equation in maple give me:

ec1:= diff(R(rho), rho, rho)+(diff(R(rho), rho))/rho+(d/rho+k^2-m^2/rho^2)*R(rho) = 0;
dsolve(ec1)

R(rho) = _C1*WhittakerM(-(1/2*I)*d/k, m, (2*I)krho)/sqrt(rho)+_C2*WhittakerW(-(1/2*I)*d/k, m, (2*I)krho)/sqrt(rho)

I need to normalize this function in order to find the constant and solve the Schrodinger equation but I don't know how.

Thanks in advance.

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    What exactly do you mean by normalizing? That the magnitude of $R$ is equal to 1? – 2017-02-28
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    It might help to know which system your equation is supposed to model e.g. hydrogen atom, helium atom, harmonic oscillator etc. That may allow someone to verify your stated equation, which appears to be for the radial part of the wavefunction only. – 2017-02-28
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    What are the two conditions? – 2017-02-28
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    Is this a *mathematics* question, or instead a programming question? (If the latter, it belongs on a different site.) – 2017-02-28
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    @DavidG.Stork It's not always obvious where you ask Maple questions but there is a Maple tag here. – 2017-03-01

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