I am trying to find proofs of the stability of an atom, says, for simplicity, the hydrogen atom. There are positive answers and negative answers in various atom models.

The naive "solar system" model of a negatively charged electron orbiting the positively charged nucleus is not stable, it radiates electro-magnetic energy and will collapse.

The Bohr-Sommerfeld atom model seems to make stability a postulate.

The Schroedinger equation seems to give a "proof" of the stability of the hydrogen atom, because we have stable solutions corresponding to bound states.

Does anybody know if the Dirac equation or Quantum Electro-Dynamics can be used to prove teh stability of a hydrogen atom?

Many thanks in advance for any references where I can learn more about this.

I am trying to find proofs of the stability of an atom, says, for simplicity, the hydrogen atom. There are positive answers and negative answers in various atom models.

The naive "solar system" model of a negatively charged electron orbiting the positively charged nucleus is not stable, it radiates electro-magnetic energy and will collapse.

The Bohr-Sommerfeld atom model seems to make stability a postulate.

The Schroedinger equation seems to give a "proof" of the stability of the hydrogen atom, because we have stable solutions corresponding to bound states.

Does anybody know if the Dirac equation or Quantum Electro-Dynamics can be used to prove the stability of a hydrogen atom?

Many thanks in advance for any references where I can learn more about this.