Do Photons Emit When Electron's Energy is Measured?

In summary, the emission of photons from hydrogen atoms is related to the electron's energy levels, which are in a linear combination of eigenstates. This means that when a photon is emitted, it corresponds to a measurement of the electron's energy. The interaction between the electron and the electromagnetic field results in a superposition of EM photon states, and measuring the photon will give information about the electron's state. This can be seen as a form of entanglement between the electron and the photon.
  • #1
Manchot
473
4
Hey all,

I'm currently in my second QM class, and I have a question about the emission of photons. Last semester, as we studied the wavefunction of a hydrogen electron, the professor briefly mentioned that the energy levels correspond to the observed energies of photons emitted from hydrogen atoms. In general, however, an electron will be in a linear combination of the eigenstates. Since the photon energies are only measured to be discrete, does this mean that the emission of a photon corresponds with a measurement of the electron's energy?

NB: I haven't learned QED yet, so please give me a dumbed-down answer. Thanks. :biggrin:
 
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  • #2
It measures what the electron's energy was before the radiation since
h\nu=E_i-E_f.
 
  • #3
Manchot said:
In general, however, an electron will be in a linear combination of the eigenstates. Since the photon energies are only measured to be discrete, does this mean that the emission of a photon corresponds with a measurement of the electron's energy?

Yes! Picture it this way: the superposition of electron eigenstates, through the interaction with the EM field, will result in a superposition of the EM photon states, where each of the terms corresponds to each of the eigenstate-transitions in the hydrogen atom.
And now you measure, and see one of those photons (application of the measurement postulates).

Symbolic example:

|H-atom> = |psi3> + |psi5>
(say, superposition of the third and fifth excited state, just for the sake of it).

Interaction with EM field (from the vacuum state) gives you:

|H-atom+EM field> = a |psi0> |photon3> + b |psi0> |photon5> + c |psi1> |photon2> + ...

where the first state in each term gives you the "final" state of the H-atom, and the second state in each term gives you the EM field state (kind of photon you have).

Now you do a "photon" measurement, so, with probability |a|^2, you have the first state (ground state + photon3), with probability |b|^2 you have the second state (ground state + photon5), ...
 
  • #4
Ah, so the photon itself is in a superposition of eigenstates. For some reason, I never considered that possibility. Does that mean that you can determine the state of the electron by measuring the energy of the photon? Is that a form of entanglement?
 

1. How does the energy of an electron affect the emission of photons?

The energy of an electron can affect the emission of photons in a few different ways. When the energy of an electron is measured, it can change the electron's energy state, causing it to emit a photon. Additionally, when an electron loses energy, it can also emit a photon. This is known as spontaneous emission. The energy of the electron can also determine the frequency or wavelength of the emitted photon.

2. Is the emission of photons a random process when measuring an electron's energy?

Yes, the emission of photons when measuring an electron's energy is a random process. This is because the exact energy level of the electron cannot be predicted, and therefore the exact energy of the emitted photon cannot be predicted either. However, the probability of the electron emitting a photon at a certain energy level can be calculated using quantum mechanics.

3. Can photons be emitted from an electron without any external stimuli?

Yes, photons can be emitted from an electron without any external stimuli. This is known as spontaneous emission and occurs when an electron transitions from a higher energy state to a lower energy state, releasing a photon in the process.

4. How does the emission of photons when measuring an electron's energy relate to the uncertainty principle?

The uncertainty principle states that it is impossible to know both the exact position and momentum of a particle at the same time. When measuring an electron's energy, the act of measurement disturbs the electron's state, making it impossible to accurately know its energy level and position simultaneously. This disturbance can also cause the electron to emit a photon, adding to the uncertainty of the measurement.

5. Can the emission of photons when measuring an electron's energy be controlled or manipulated?

Yes, the emission of photons when measuring an electron's energy can be controlled and manipulated. This is done through techniques such as stimulated emission, where an external photon is used to induce the emission of additional photons from the electron. This process is used in technologies such as lasers and LED lights.

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