|Apr13-05, 02:35 PM||#1|
3 easy QFT questions
I have three questions about QFT. I know you can answer this questions, sure you can.
- How does a standing wave look like in 3 dimensions (x,y,z). I mean an electro magnetic oscillation between two walls or in free space. I can't really imagine that thing and looked for pictures (google) but coudn't find what I searched for.
- Let's say we have an electromagnetic oscillation with quantum number n=3. Then this has energy of 7/2*w*h(bar) and contains 3 particles (photons).
Here we say this particles make the field oscillating. And thus the oscillation of this particles can go from earth to moon. But if we describe this 3 photons as wave packets they don't have such an influence (from moon to earth). Something has to be false, but what?
- Consider two plates. Between that plates there is a harmonic oscillation with energy 7/2*w*h(bar). How can we describe this oscillation with formulas. I tried to solve this with 2 wave functions. One comes from left and one from the right side and they interfer. But my wave functions don't involve the energy, arghhhhh. Can someone give me a guess?
Thanks for any help.
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|Apr13-05, 02:53 PM||#2|
or google for standing wave animation
These phonons do not make any field oscillate, they are the actual result of the oscillations of a massless spin 1 field. Well, actually they arise as the oscillations of a massive spin 1 field (with certain energy value that corresponds to the given energy), and then the mass is taken to be ZERO.
|Apr13-05, 03:42 PM||#3|
|Apr13-05, 05:31 PM||#4|
3 easy QFT questions
|Apr14-05, 06:41 AM||#5|
QFT is usually described in perturbation theory usiing Feynman diagrams.
In this case, the created photons are plane (or spherical) wave trains.
They don't really propagate in space, because having a defiinite momentum, the wave train is infinite and exists thoughout all space. They are best seen in the momentum representation. A physical photon with a finite extent in space would be a linear combination of these photon states forming wave packet, just as a classical EM wave packet is formed. So photon wave packets can be wave packets in QED, formed in the same way wave packets are formed in EM.
|Apr14-05, 08:17 AM||#6|
We need to make a clear distinction between real and virtual photons here
Again this can lead to a discussion on semantics
Though it is really important to realize that photons arise as the actual vibrations of the spin 1-field (you can call this the actual wave indeed). But it needs to be said that when the field 'goes' from one vibration-mode to another, the change in energy corresponds to the actual photon. Not the wave itself...
That is the big difference between QM and QFT
|Apr14-05, 08:25 AM||#7|
thanks you both.
I tried to calculate a harmonic oscillation in free space. I did this by letting one wave come from the right side and one from the left (superposition between these two waves gives me an oscillation):
That's the expression with no energy. For the expression with energy I did this:
now k=p/h(bar) (1)
thus: p=E/c and with (1) and the definition m=E/(c*h(bar)) the wavefunction p(x,t) goes into:
And if I take the superposition of these two waves I get the oscillation:
And if the oscillation is in the ground state the factor m transforms because
And the w in the wavefunction is the same w as the w in the energy expression for the ground state.
Is this right?
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