It is often stated that quantum mechanics is able to explain the stability of atoms. I think most explanations are cheating b/c the compare apples and oranges. There are two reasons in classical theory which indicate that atoms should be unstable: A) there is no minimum for the orbit; the radius r can become arbitrary small, therefore the potential energy V(r) is not bounded from below B) due to emission of electromagnetic waves the electron will lose energy and will therefore fall into this unbounded potential V(r) QM solves (A); the eigenvalue problem is well-defined; the spectrum of H is bounded from below; there exists a stable ground state; therefore the potential energy <V> is bounded from below. However QM does not solve (B), simply b/c there is no dynamical el.-mag. field; QM is not even able to state the problem (B). Of course there are attempts to address this scenario in QED; the most famous one is the (perturbative!) Lamb shift calculation. So here's my question: is there a non-perturbative proof (in the physical sense ;-) which answers (B) in the affirmative?