I have read this question:
where Kurshal Shah in a comment says:
As per the energy-time uncertainty relation, the emitted photon does not have a definite energy, but a spread. You need to account for that too.
where Ben Crowell says:
Let's say an isolated atom emits a photon. The excited state in the atom has some lifetime τ. Through the energy-time uncertainty relation, that gives the excited state some uncertainty in energy δE∼h/τ (not the same as ΔE, which is a difference in energy between atomic states). The photon then has the same uncertainty δE in its energy, which corresponds to an uncertainty in frequency. The photon isn't in an eigenstate of energy. Yes, when you measure the energy of the photon, you get a random outcome. However, there is a quantum-mechanical correlation between this energy and the energy of the atom, so that energy is exactly conserved (not just statistically, on an average basis).
Now energy must be conserved in a closed QM system.
In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time.
But if the energy of the emitted photon has some uncertainty as per QM, but the emitting atom's energy levels are specific energy levels, an excited and a ground state, then the difference between the energy levels must be a specific energy level, which should be the energy level of the photon.
Now if I detect (observe, absorb) this photon, then I will get a specific frequency, an eigenvalue. What I do not understand is, why the source of the photon, that is the emitting atom has a definite energy level difference between excited and ground state.
that gives a specific energy level difference
the photon that is emitted must have this specific energy level, since the electron lost this specific kinetic energy to go from excited to ground level
but the questions say, that the photon does have an uncertainty in its energy level
when I detect (observe, absorb) this photon, I get a certain eigenvalue
- Does the photon have a well defined frequency or not?