Some hydrogen atom exists in some excited quantum state, and after some time $\Delta t$ it's de-excited, emitting a photon carrying the energy difference.
It is claimed that this photon will carry some uncertainty with respect to its energy (and therefore, continuous energy spectrum), attributed to the uncertainty in the difference between the two hydrogen states due to the uncertainty principle.
How true is this? And how does this square with the fact that the energy values of a hydrogen orbitals are eigenvalues of the Hamiltonian, which, in principle, are completely discrete numbers?
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