Inspired by this: Electrical neutrality of atoms
If I have a wavefunction of the 'reduced mass coordinate' for a hydrogen like atom made from an electron and a positron, what is the spatial charge distribution?
When we solve the hydrogen atom, we change into coordinates of the center of mass, and the separation distance with the reduced mass. Here, the masses of the constituent particles are the same. So the center of mass is equidistant from the positron and electron, and so discussing r and -r is just swapping the particles. Since the probability distribution for all the energy levels of the hydrogen atom are symmetric to inversion (images can be seen here http://panda.unm.edu/Courses/Finley/P262/Hydrogen/WaveFcns.html ), this seems to say no matter what energy level positronium is in, the charge distribution is neutral? Since the energy level basis is complete, this seems to say we can't polarize a positronium atom without dissociating it!? This doesn't make sense to me, so I'm probably making a big mistake here.