Has anyone experimentally obtained a picture like this:

 

http://en.wikipedia.org/wiki/File:HAtomOrbitals.png

 

 

If so, where? If not, how do we actually know it's correct?

To confirm experimentally these pictures it is necessary to analyse the elastic scattering cross section. It is possible in principle. I think it has already been an object of experimental research.

 

By the way, similar pictures are valid for the positive charge in Hydrogen but they scaled down to much smaller sizes. The atomic nucleus "turns around" the atomic centre of inertia as well as the electron so there are two "clouds" of different sizes and different sign of electric charge (http://arxiv.org/abs/0806.2635).

 

Bob.