If all states are stationary, what causes atoms to radiate then?

Main Question or Discussion Point

We've solved for several systems, the hydrogen atom for instance, and one of the properties of these is that it doesn't matter what excitation state you look at, they are stationary states, the Hamiltonian is constant in time, so where's the impetus on an excited atom to radiate light if it's in a stationary state?

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Matterwave
Gold Member
The stationary states you solved for are for the hydrogen Hamiltonian only. If you included the vacuum EM field, then they would not be stationary states. All "spontaneous emissions" are the result of stimulated emissions except with the vacuum EM field.

So, what is this vacuum EM field? How does it trigger emission of light in the atom?

Bill_K
So, what is this vacuum EM field?
Include the electromagnetic field by adding the term ½(E2 + B2) to the Hamiltonian. Initially the EM field is in the vacuum state (no photons).
How does it trigger emission of light in the atom?
Add the interaction terms to the Hamiltonian:

(1/2m)(p - eA)2 + eφ

These terms have nonzero off-diagonal matrix elements which induce the transition between the excited state ψ1 and the ground state ψ0

Then I wonder, why usually an atom is in an eigenstate of H_atom, instead of an eigenstate of the full QED hamiltonian?

I always thought it was because the superposition of states was non-stationary, so if you had an ensemble of atoms with a given energy distribution, the possibility that any one could be in any of a multitude of excited states is what causes the superposition, and hence non-stationary state