How to find hydrogen wave-functions? I have found the hydrogen wave functions and would now like to calculate the function that describes the orbitals so that I can plot this function and see how they look.
I don't know how I can do that and it is crazy how I cannot find anything on the subject on the internet as if there was no relation between the wave functions and the orbitals.
Could you please tell me what I need to do to get a function $r(\theta,\phi)$ out of my wave functions $\psi(r,\theta,\phi)$.
 A: When you say

I already have derived them, I have a list of them with me. What I want is the polar equation of the corresponding orbitals.

I take it you have the wavefunctions
$$
 \psi _{n\ell m}(r,\theta ,\varphi )
={\sqrt {{\left({\frac {2}{na_{0}}}\right)}^{3}{\frac {(n-\ell -1)!}{2n(n+\ell )!}}}}
e^{-r /na_0}
 \left(\frac{2r}{na_0}\right)^{\ell }
L_{n-\ell -1}^{2\ell +1}\mathopen{}\left(\frac{2r}{na_0}\right)\mathclose{}
Y_{\ell }^{m}(\theta ,\varphi )
$$
as derived e.g. in Wikipedia, and you're looking for a representation of the form $r=f(\theta,\varphi)$. 
This is not doable in a unique way: different authors choose different ways to graphically present the behaviour of $\psi _{n\ell m}(r,\theta ,\varphi )$, and different choices give different representations.
Usually, however, the most useful graphical representation is not in an equation of the form $r=f(\theta,\varphi)$, but rather you plot the surfaces of constant $|\psi _{n\ell m}|^2$, setting the level to some (arbitrary!) probability that will make for a pretty picture. Depending on what you're after, it can be a good idea to take the real or imaginary parts of $\psi _{n\ell m}$ before making the contour plot, which will switch the azimuthal harmonic from $e^{im\varphi}$ to sines and cosines, and thereby bring in more information into the plot.
