Quantum system can emit only photons with energy equal (within
the uncertainty) to the difference between two energy states.
Even if the atom is in a superposition of energy states
\left|\Psi\right> = C_0 \left|0\right> + C_1 \left|1\right> +
C_2 \left|2\right> + \ldots \qquad (1) with average energy
somewhere between the levels, it can emit only certain set of
photons: $E_1 - E_0$, $E_2 - E_0$, $E_2 - E_1$ etc. Emission of
a photon is an act of measurement since the energy of the
emitted particle contains information about the atom. If the
energy of the photon is $E_2 - E_1$ then the energy of the
electron in the atom is $E_1$ - the energy of the final state of
the transition. The next photon emitted by this atom will have
energy equal to $E_1 - E_0$ for sure. If one observe photons
emitted by an ensemble of atoms in state (1) he will see $E_1 -
E_0$ photons with probability $\left|C_1\right|^2$, any of $E_2
- E_0$ and $E_2 - E_1$ with probability $\left|C_2\right|^2$ and
so on. The total energy emitted by t