I remember from introductory Quantum Mechanics, that hydrogen atom is one of those systems that we can solve without too much ( embarrassing ) approximations.
After a number of postulates, QM succeeds at giving right numbers about energy levels, which is very good news.
We got rid of the orbit that electron was supposed to follow in a classical way ( Rutherford-Bohr ), and we got orbitals, that are the probability distribution of finding electron in space.
So this tiny charged particle doesn't emit radiation, notwithstanding its "accelerated motion" ( Larmor ), which is precisely what happens in real world.
I know that certain "classic questions" are pointless in the realm of QM but giving no answers it makes people asking the same questions over and over.
- If the electron doesn't follow a classic orbit, what kind of alternative "motion" we can imagine?
- Is it logical that while the electron is around nucleus it has to move in some way or another?
- Is it correct to describe electron motion as being in different places around nucleus at different instants, in a random way?