when I was new into quantum mechanics, I thought we can describe helium atom by two wavefunctions - one for every electron. After some time I discovered how wrong I was - first, because electrons are indistinguishable we can't say 'this' electron now is here and after time it will be here, second - we take wavefunction and antisymetrize it to obtain the Pauli Exclusion Principle.
Okay, that was only an introduction. What should we do if we would like to get a full description of hydrogen atom, let's say in Dirac's equation formalism (assuming proton is elementary particle, we don't want to mess with QCD yet - if somebody has problem with that he can use positron or antimuon)? Of course the standard procedure is to get only an electron and potential from proton, maybe if we want to be super-detalic we can write another Dirac equation for proton (still spin 1/2) and perturb it by attraction from electron. But it's still not full description.
Any ideas, answers, links to handbooks? Or is it open problem? I'm not looking for calculation method, only for theoretical proposition for equation.