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.