# Trying to understand how spontaneous emission works

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• Groucho
In summary, Gerald Folland's book "Quantum Field Theory: A Tourist Guide for Mathematicians" is about a nonrelativistic particle of mass M and a scalar field with quanta of mass m and the state space for the particle is L^2(T^3) for a 3-torus T^3 and the state space for the field is the Boson Fock space over L^2(T^3), and he describes the Hamiltonian for the particle, for the field, and for the interactions, and then starts calculating the expected time interval for the emission of a field quantum.
Groucho
I'm reading Gerald Folland's "Quantum Field Theory: A Tourist Guide for Mathematicians" and I'm up to Section 6.2 which is called "A toy model for electrons in an atom". He has a nonrelativistic particle of mass M and a scalar field with quanta of mass m and the state space for the particle is L^2(T^3) for a 3-torus T^3 and the state space for the field is the Boson Fock space over L^2(T^3), and he describes the Hamiltonian for the particle, for the field, and for the interactions, and then starts calculating the expected time interval for the emission of a field quantum. So you start with the state corresponding to the particle in energy state n and no field quanta present, then apply the time evolution operator U(t) for some specific t>0, then apply the linear functional corresponding to the state where the particle is in state m and there is one field quantum present with momentum p, and the modulus squared of the result gives you the transition probability. I am trying to understand better how this actually links with actual experimental results.

Can we make sense of the idea of just staring constantly at a hydrogen atom and waiting to see if anything happens, is that an experiment that is actually feasible to do? I vaguely remember reading somewhere that if you do that then emission of a photon will not happen. Am I wrong about that?

Thanks, can you tell me more about the debunking? I can't find discussion of the debunking in the Wikipedia article.

It seems as though to give an account of spontaneous emission of photons in a sample of excited hydrogen atoms you would have to give some kind of account of when collapse of the wavefunction takes place. Has work been done on this?

Groucho said:
Can we make sense of the idea of just staring constantly at a hydrogen atom and waiting to see if anything happens, is that an experiment that is actually feasible to do? I vaguely remember reading somewhere that if you do that then emission of a photon will not happen. Am I wrong about that?
If you just stare, it will not influence the atom. But if you repeatedly probe the atom to check out if it has decayed, then you can really slow down the emission. Probing involves an active interaction with the atom, so it should not be surprising that it can influence the atom behavior. This is the real quantum Zeno effect, which has been verified experimentally.

bhobba
dextercioby said:
You mean the Quantum Zeno Effect? It's been debunked already, as it's based on a misinterpretation of von Neumann's collapse postulate.
If you mean the Ballentine's debunking of the quantum Zeno effect, I have to tell that the Ballentine's debunking has been debunked, as he himself misinterpreted the collapse postulate. The quantum Zeno effect is a real effect observed in laboratories.

bhobba
I didn't mean Ballentine's book, but some notes I found online from the famous Robert Geroch from the University of Chicago. I don't have them on my PC anymore and couldn't find them online :(

dextercioby said:
I didn't mean Ballentine's book, but some notes I found online from the famous Robert Geroch from the University of Chicago. I don't have them on my PC anymore and couldn't find them online :(
In the absence of those notes, I can only tell that Geroch is an expert for mathematical physics, but not an authority for conceptual questions such as wave function collapse.

And who could you define to be an authority in this domain?

dextercioby said:
And who could you define to be an authority in this domain?
Like in any other domain, by having a lot of published papers (in that domain), by receiving a lot of citations of those papers, by being frequently invited as an invited speaker at respectable conferences (in that domain), etc. (It is not required that everybody agrees with the ideas expressed in those papers.)

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## 1. What is spontaneous emission?

Spontaneous emission is a process in which an atom spontaneously releases energy in the form of a photon without any external stimulation or influence.

## 2. How does spontaneous emission occur?

Spontaneous emission occurs when an excited atom or molecule returns to its ground state, resulting in the release of energy in the form of a photon.

## 3. What is the significance of spontaneous emission in physics?

Spontaneous emission plays a crucial role in understanding the behavior of atoms and molecules, especially in the fields of quantum mechanics and spectroscopy.

## 4. What factors affect the rate of spontaneous emission?

The rate of spontaneous emission is affected by the energy difference between the excited and ground states, as well as the density of states and the polarization of the emitted photon.

## 5. Can spontaneous emission be controlled or manipulated?

While spontaneous emission is a fundamentally random process, it can be influenced by external factors such as temperature, pressure, and electromagnetic fields. This allows for some control and manipulation of the rate and direction of emitted photons.

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