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## Exciting a photon

Wikipedia is not that great a reference - and that quote is does not actually contradict what I've been trying to say. You also have not shown how this model takes into account the other comments and questions I have referenced. Have you done the math? [1]

The particle-in-a-box model can be solved analytically fersure - but it is not a good model of actual physical systems. It is especially problematic for light, since you have to figure out what the box is made out of that would confine a single photon without it annihilating at the walls. When it comes to energy eigenstate transitions, you still have to figure how that would come about. i.e. what would be the physical process that changes the width of such a strange box? Not everything describable in math is physically possible.

You can confine a photon gas in a box though.
This uses a model where photons are constantly being annihilated and created.
In this case, you can raise the mean and total energy of the system by changing the width of the container. But what is it that happens to individual photons?

You could be imagining a single photon bouncing between ideal, perfectly reflecting, walls [2]. In which case, the photon is being annihilated at each wall, and then a new one is created. (Though there is some philosophical hair-splitting over this point.) It is possible to arrange for the photon thus created to be a higher frequency than the one annihilated. I would assert that this process does not well fit the concept of "exciting a photon": it kinda means that it is the same photon that has more energy like an excited electron-in-a-box is the same electron.

For a single particle in a box, when you make the box smaller, the energy eigenstates raise in value, and so does the expectation value of a measurement of energy of the system. The particle, however, is not in a single energy eigenstate until a measurement of energy has been made. You can figure out the odds by expanding the initial eigenstate wave-function in terms of eigenstates of the final potential.

So the process would involve two steps - making the box smaller, and then measuring the energy level. For a perfectly reflecting box of one photon (as discussed) how would you (or the system) conduct that measurement without annihilating the photon?

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[1] see this example for what happens when you change the width of a confining potential.
The author has the potential increasing in width, and finesses the system so there is an eigenstate in the final system with the same energy as the ground state of the initial system. As an exercise, do the problem the other way around - making the box smaller.

[2] You realize that reflection, at the photon level, is described using creation and annihilation operators right? The law of reflection is only obeyed on average and all that?
(In fact D Simanek has a pmm puzzle using the idea of a photon bouncing between perfect reflectors.)

 @phinds +1 that! I have been resisting the pun from the start :)

 "It's nature that is bizzare, not the physics."
No, it are humans that are ill-informed, not nature nor the physics are bizzare.

 The particle-in-a-box model can be solved analytically fersure
The "quantum profile" of the hydrogen atom can also be solved analytically, which is seemingly a miracle since 70% (is that figure right?) of the universe is hydrogen. Of course, you get to helium and above, or maybe even deuterium, and you're forced to use the Runge-kutta matlab function and solve these problem numerically. In any case, doesn't anybody think its weird how electron orbitals manifest from the Shrodinger equation? It is bizzare, solving the radial and azimuthal equations yield these weird Legendre polynomials, and we infer the quantum numbers from co-efficients in the Euler exponents. I mean, who'd of thunk?

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Even then - "particle in a box" is not a good model for the H atom.

74% yes. I don't know about "miracle" but it is certainly useful.
Helium is sort of doable - it's a common exercise for senior undergrads.
This allows for approximations for hydrogenic and helium-oid atoms ... varying success.
Anything else does, indeed, require a numerical method. Matlab is common for a first pass - but you end up learning to program in something like c++ since the inner workings of matlab are a secret. But this is for another thread. "Rung-Kutta" tends to imply a shooting method - there are faster methods .. also for another thread.

 No, it are humans that are ill-informed, not nature nor the physics are bizzare.
+1. I noticed that too - "common sense" is what tells you the World is flat.

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 Quote by Simon Bridge "Rung-Kutta" tends to imply a shooting method - there are faster methods .. also for another thread. .
To which I must add the best (not much competition) line ever in a numerical methods book ("Numerical Recipes" series), summing up the authors' recommendation for partial differential equations: "shoot first, then relax".

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 Quote by Naty1 I think it does affect energy...for example: http://en.wikipedia.org/wiki/Particle_in_a_box
It is not that easy for photons. For photons, the particle in a box problem is realized by microcavities or micropillars. This way the box is realized by highly reflective mirrors like distributed Bragg reflectors, effectively placed half a target wavelength away from each other. However, the reflectivity of this kind of mirror cannot be broadband and you get some narrow wavelength range of good reflectivity around the target wavelength.

If you now change the resonance wavelength by changing the distance of the mirrors, the microcavity becomes a low-reflectivity cavity for the prior resonance wavelength and photons inside will simply escape. Experiments like that have been done with acoustic strain pulses and semiconductor microcavities.

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Simon:
 The particle-in-a-box model can be solved analytically fersure - but it is not a good model of actual physical systems.
agreed....too idealistic

 You could be imagining a single photon bouncing between ideal, perfectly reflecting, walls [2]. In which case, the photon is being annihilated at each wall, and then a new one is created. (Though there is some philosophical hair-splitting over this point.) It is possible to arrange for the photon thus created to be a higher frequency than the one annihilated. I would assert that this process does not well fit the concept of "exciting a photon": it kinda means that it is the same photon that has more energy like an excited electron-in-a-box is the same electron.
I get the idea of your objection....I think your points better than mine....

I have simply taken such explanations as I posted at face value...never really questioned them....I just took the view such an explanation is a simple extension of quantum confinement...

I just skimmed Albert Messiah QUANTUM MECHANICS Chapter 3 regarding one dimensional quantized systems....[which I had in mind when I posted] to criticize my own post:

....there are no one dimensional systems,
....If the potential well is finite, there is a finite probability of the wave function NOT being reflected,
....If the potential well is infinite there is complete reflection and the energy levels are quantized....and we can't do infinite anything.

So what about the PeterDonis explanation I posted...??

As a related suggestion, how about collapsing space-time to 'rev up a photon'??
[If cosmological distance expansion redshifts radiation, seems like cosmological contraction should blue-shift??]

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In another discussion:

Brian Cox claims changing the energy level of a particle changes the energy level of all its counterparts...So maybe all I have to do to excite all photons is to turn on a light bulb?

Issue: Brian Cox on TV claimed…..no two electrons anywhere in the universe can be in precisely the same energy levels…. claimed to be changing the state of all electrons in the universe by warming up a diamond….a consequence of the Pauli exclusion principle proven in 1967.

Synopsis [one view] :

Without knowledge of Pauli's Exclusion Principle one might expect electrons arbitrarily far away from one another to have identical energy levels. Pauli, however, shows that is simply impossible.

Likely too theoretical considering the OP question, but not so easily dismissed as I thought before the discussion.

 Without knowledge of Pauli's Exclusion Principle one might expect electrons arbitrarily far away from one another to have identical energy levels. Pauli, however, shows that is simply impossible.
That's hogwash Naty, didn't you read that long thread on PF where Cox actually got into the argument himself? I don't buy his argument for a second...that a hydrogen atom somewhere in the andromeda galaxy has its electron energy levels arranged differently than a hydrogen atom planted in my left cheek. This would require an impossibly absurd number of energy levels in the tiny space of a given hydrogen atom (on the order of 10^-12m).

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 didn't you read that long thread on PF where Cox actually got into the argument himself?

I'll have to catch up on it later today.

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 That's hogwash Naty...
Could turn out that way,of course, but it IS what is being taught in at least one university....

I stand by my prior post:

 Synopsis [one view] : Without knowledge of Pauli's Exclusion Principle one might expect electrons arbitrarily far away from one another to have identical energy levels. Pauli, however, shows that is simply impossible.
That interpretation seems disputed by some, but not refuted.....good!

 As atyy and others have pointed out, what Brian Cox said can be considered technically correct. But as Ken G and others have pointed out, it's important how formal QM is translated into ordinary language, because its precise relationship to nature is very much a matter of interpretation.
When particles can be teased into existence via cosmological horizons, observer acceleration, or the acceleration of space-time, there seem to me to be some sort 'spooky action at a distance'...and that seems to be the main debate issue in the BeCox thread. A closely related issue is how our approximate, simplified, mathematical models [like BeCox] apply to the observational world...and whether they apply at cosmological distances.

Anyway, I'm not knowledgeable enough to take a firm position one way or the other; but I am knowledgeable enough to keep an open mind.

 Anyway, I'm not knowledgeable enough to take a firm position one way or the other; but I am knowledgeable enough to keep an open mind.
That's just the point, it has little to do with being "knowledgeable" or not, IMO, it has to do with common (folk) sense. My belief is that we take this wave function thing too seriously because, at this moment in the dark ages of physics, we don't have a better alternative. The result is that people actually try to convince themselves that this "quantum weirdness" is actually reality, when, I can assure you, a model will come by probably sooner than later that's gonna make us all feel silly for believing this stuff.
 You can give more energy to a photon, for instance by inelastic scatterings: Raman scattering, inverse Compton scattering. In these processes the photon is not simply absorbed and reemitted. One also have photon-photon scattering (Delbrück scattering) and I think that in principle the photons can exchange energy. Maybe somebody from high-enegy physics can give us a definite answer.

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 Quote by DiracPool My belief is that we take this wave function thing too seriously because, at this moment in the dark ages of physics, we don't have a better alternative.
When we answer questions in PF, there is this, infrequently spoken, rider that we are answering in terms of some implied model. It's reasonable to take the particular model seriously - if this were a question in high-school kinematics, we'd be taking Newtonian physics seriously.

 Quote by soarce You can give more energy to a photon, for instance by inelastic scatterings: Raman scattering, inverse Compton scattering. In these processes the photon is not simply absorbed and reemitted. One also have photon-photon scattering (Delbrück scattering) and I think that in principle the photons can exchange energy. Maybe somebody from high-enegy physics can give us a definite answer.
The Feynman diagram for photon-photon scattering involves the photons being destroyed (they turn into particle-antiparticle pairs) and then getting recreated after a short interval. It's probably a philosophical point as to whether the exiting photons are the same photons as the incoming ones.

(recall - time is vertical axis and space is horizontal)

Would this be good enough to call "photon excitation" (see post #1) though?
If we'd changed the kinetic energy of a free electron by scattering off another electron, would we call that "excitation" of the electron?

Raman Scattering: is the inelastic scattering of a photon ... why not include Rayleigh scattering, which is the same thing, only elastic? Either way, the Feynman diagram similarly requires the photon to be destroyed and a new one created... the scattering particle first absorbs (annihilates) the photon, gaining energy, holds onto it for a bit, then releases the energy as another photon. If some of the energy dissipates by another means in the meantime, then less energy is available to be released.

Inverse Compton scattering is the same process in a different context - this is where low-energy photons are scattered to higher energies by relativistic electrons. Again, the electron absorbs the photon, gaining energy, and, after a bit, releases energy as a different photon. In this case it releases more energy that it received because of the context in which it happens.

Remember what I said earlier about implied models?

When we confine, say, an electron to a potential well, what we are actually doing is bombarding it with photons. But it is hard to talk about the process in such detail so we talk about potentials instead and so we don't have to look at each individual ##e^- - \gamma## interaction.

But the moment the question involves photons, explicitly, we are in a different model-framework where it is difficult to see how the language of energy level transitions applies.

I'm hoping a visiting science adviser can be more clear than me.

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 Quote by Naty1 have simply taken such explanations as I posted at face value...never really questioned them....I just took the view such an explanation is a simple extension of quantum confinement...
I can easily understand how you could end up doing that - the way beginning QM texts are written, you'd think all these transitions etc happen by magic. There is always a physical process involved - the idea is to use the model that best fits the process you are looking at (or develop one.)
 I just skimmed Albert Messiah QUANTUM MECHANICS Chapter 3 regarding one dimensional quantized systems....[which I had in mind when I posted] to criticize my own post: ....there are no one dimensional systems, ....If the potential well is finite, there is a finite probability of the wave function NOT being reflected, ....If the potential well is infinite there is complete reflection and the energy levels are quantized....and we can't do infinite anything.
How you get a 1D system is to make the other two dimensions very very big, so the energy levels are quantized in one dimension only.
You can approximate something to an infinite square well if you are dealling with the low-energy configuration of a big potential - then the penetration beyond the classical limits can be safely ignored.
This sort of thing is done a lot in solid state physics.
 So what about the PeterDonis explanation I posted...??
What? Where? <looks>
Oh the gravitational blue shift - I thought that was addressed by Peter?

 As a related suggestion, how about collapsing space-time to 'rev up a photon'?? [If cosmological distance expansion redshifts radiation, seems like cosmological contraction should blue-shift??]
One way to confine a photon would be to have a closed space-time ... this gives you periodic boundary conditions based on some metric.

But you'd still be faced with the problem of having to "excite" the photon to a new energy level without destroying it... you've proposed somehow having the closed space-time region shrink somehow. How? There's just a photon in it. Anyway, making a whole new universe is cheating :D

There are several ways to use gravity to trap photons. Supermassive black holes spring to mind. Space-time inside one is pretty um hard to think about. Considering GR topology requires field theory I think, rather than the photon-QM/Wave mechanics we've been using ...
 In another discussion: http://www.physicsforums.com/showthread.php?t=561511 Brian Cox claims changing the energy level of a particle changes the energy level of all its counterparts...So maybe all I have to do to excite all photons is to turn on a light bulb?
Cox's argument involves the Pauli exclusion principle ... not everything obeys it. Cox's example was electrons, which do. Photons don't.

Possibly what you've been thinking of is electromagnetic standing waves in a waveguide?

 Quote by Simon Bridge When we answer questions in PF, there is this, infrequently spoken, rider that we are answering in terms of some implied model. It's reasonable to take the particular model seriously - if this were a question in high-school kinematics, we'd be taking Newtonian physics seriously.
I wouldn't take too seriously the models, it doesn't have to be associated to a real process. One use model to calculate things and compare them with the experiments.

 The Feynman diagram for photon-photon scattering involves the photons being destroyed (they turn into particle-antiparticle pairs) and then getting recreated after a short interval.
Anybody measured the short interval between absorbtion and reemission of the photon?
All those processes involve virtual states and, as far I know, the scattering take place instantaneously. The picture that the photon is absorbed, the system holds on for a while and then reemits the photon is wrong.

By "exciting a photon" he probably ment giving energy of a photon.

 It's probably a philosophical point as to whether the exiting photons are the same photons as the incoming ones.
I agree. Based on Feynman diagram model the photon itself may go through a virtual electron-positron pair... It maintains its identity or it keeps changing ? :)

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