I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for $\ell=0$ using the WKB approximation. I am sure that I set up the integral properly, I am just a little confused as to how to find the limits. My integral is

$$ \int \sqrt{2m \left( E + \frac{e^2}{r}\right)}dr = \left( n + \frac 1 2\right) \hbar \pi. $$

would it be

$0\ to\ r_0? $


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