I'd like to calculate the probability density for Hydrogen in the $|2,1,1\rangle$ and $|2,1,-1\rangle$ states. There is an $\exp(\pm i\phi)$ term attached to the wave function for these states. It seems to me that $|\Psi|^2$ in this case would be the same for $|2,1,1\rangle$ and $|2,1,-1\rangle$ since $|\exp(i\phi)| = 1$ with the same being true for $|\exp(-i\phi)|$. Where am I going wrong here?
Also, since I'm working in spherical coordinates the PD should be $r^2|\Psi|^2$, right (this will result in those classic energy orbital diagram functions)?