I recently though about photons emitted in a spontaneous atomic transition. These states have a definite energy as they are eigenstates of the hamiltonian, however a photon emitted by an electron going through state 1 to state 2, has not a perfectly defined energy E = E1 - E2, as then the frecuency (energy) would be completely defined and the uncertainty in position (time) would be infinite.
I have found that these emission lines has a finite width and that the photon has some uncertainty in energy, but theoretically the states has perfectly defined energies, then if a photon carry slightly more energy than that of the emission line, where is this energy coming from? Is this because the quantum theory used is non-relativistic?
