Number of nodes in Hartree-Fock solution

The Hartree-Fock equation for atoms is of the form 


$\left(\frac{d}{dr^2}+f(r)-\epsilon\right)P(r)=g(r) \tag1$ 


Usually algorithms to solve this equation assumes that the number of nodes of $P(r)$, $n\_r$, is of the form
$$n\_r=n-l-1 \tag2$$ 


where $l$ is the orbital quantum number and $n$ the principal quantum number.
For closed shell $(1)$ is spherical symmetric so $(2)$ is justified. 


What about non closed shell, what is the theoretical justification for $(2)$?


