quantum mechanics - Hydrogen radial wave function infinity at $r=0$

Sunday, March 12, 2017

When trying to solve the Schrödinger equation for hydrogen, one usually splits up the wave function into two parts:

$$\psi(r,\phi,\theta)= R(r)Y_{l,m}(\phi,\theta).$$

I understand that the radial part usually has a singularity for the 1s state at $r=0$ and this is why you remove it by writing:

$$R(r) = \frac{u(r)}{r}$$

But what is the physical meaning of

$$R(r=0) = \infty~?$$

Wouldn't this mean that the electron cloud is only at the centre of the atomic nucleolus?

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