Calculating Light Scattering from Glass - QED Explained

[RedX]

I've worked out the scattering of a photon off an atom. Now I'm trying to figure out how I can use the same formulas to figure out scattering off a material. Suppose you have a light photon incident normal to a piece of glass. Classically it should go straight through or get reflected straight back up. Quantum mechanically it can be scattered in all sorts of directions or it can go straight through. So how would I go about calculating where the photon will come out? I wouldn’t have to sum over all paths because not all paths would take the same time. It seems complicated because not only can the photon also be absorbed and not scattered on the way (and when this happens how does the electron’s energy get into vibration of the atom?), but you have to keep track of whether the photon is LHC or RHC after each scatter – oh and by the way did I say that photon can just go straight through at the speed of light in vacuum, making it difficult to decide which paths to sum because variable speeds and variable paths make variable times?

Lastly, what is QED? I thought QM contained electrodynamics.

 

[chroot]

You'd have to use QED to fully understand the phenomenon. QED is quantum electrodynamics, the quantum-mechanical description of the interaction of light and matter. It is, as you said, a branch of quantum mechanics.

- Warren

 

[ZapperZ]

Originally posted by RedX
I've worked out the scattering of a photon off an atom. Now I'm trying to figure out how I can use the same formulas to figure out scattering off a material. Suppose you have a light photon incident normal to a piece of glass. Classically it should go straight through or get reflected straight back up. Quantum mechanically it can be scattered in all sorts of directions or it can go straight through. So how would I go about calculating where the photon will come out? I wouldn’t have to sum over all paths because not all paths would take the same time. It seems complicated because not only can the photon also be absorbed and not scattered on the way (and when this happens how does the electron’s energy get into vibration of the atom?), but you have to keep track of whether the photon is LHC or RHC after each scatter – oh and by the way did I say that photon can just go straight through at the speed of light in vacuum, making it difficult to decide which paths to sum because variable speeds and variable paths make variable times?

Lastly, what is QED? I thought QM contained electrodynamics.

Unfortunately, the problem of light in a material isn't as simple as you thought. There is a whole section of research in condensed matter physics devoted to optical conductivity in solids. It isn't simply a "tunneling" problem. It involves whether the material has free electrons as in metals (light interaction with plasmons), whether the material has optical phonon modes for absorption, etc. You will find that even in the so-called transparent medium, it is often not the same photon that went through the medium that gets transmitted.

A solid state text such as Ashcroft and Mermin will have a good intro on optical conductivity in materials. A more in-depth and complete treatment of this is typically found in a many-body physics text such as the one by Mahan.

Zz.

 

[RedX]

Originally posted by ZapperZ
Unfortunately, the problem of light in a material isn't as simple as you thought. There is a whole section of research in condensed matter physics devoted to optical conductivity in solids. It isn't simply a "tunneling" problem. It involves whether the material has free electrons as in metals (light interaction with plasmons), whether the material has optical phonon modes for absorption, etc. You will find that even in the so-called transparent medium, it is often not the same photon that went through the medium that gets transmitted.

A solid state text such as Ashcroft and Mermin will have a good intro on optical conductivity in materials. A more in-depth and complete treatment of this is typically found in a many-body physics text such as the one by Mahan.

Zz.

I wasn't aware that light scattering was a tunneling problem. Not sure I see how - I'll think about it more.

Optical phonon modes for absorption - what's a phonon? I was looking at how an electron can emit a photon when the electron doesn't have +-1 angular momentum about the axis of emission, and came to the conclusion that it can't otherwise angular momentum wouldn't be conserved since photons can only have +-1 angular momentum. Is a "phonon" a particle that's emitted to conserve angular momentum ( in case the electron has +-2 or 0 angular momentum about an axis) and linear momentum? If a phonon has angular momentum, then how is scattering predicible unless phonons are predicitible?

When you say that it's not the same photon that goes through that gets transmitted in a transparent material, you're not talking about photons which are absorbed and scattered in the same direction as the incident beam right? You're talking about the photons which never get absorbed at all not being the same photons? Do you mean that because photons are bosons some atoms in the excited state will emit a photon to the same state and something later happens with the original photon?

So do I have to understand QED first to understand condensed matter optical conductivity in solids? And any recommendations on a good QED book? All my quantum mechanics consists of the Feynman Lectures Volume 3 - I know almost everything in the book and nothing else: should I read Feynman's QED book?

 

[ZapperZ]

Originally posted by RedX
I wasn't aware that light scattering was a tunneling problem. Not sure I see how - I'll think about it more.

Optical phonon modes for absorption - what's a phonon? I was looking at how an electron can emit a photon when the electron doesn't have +-1 angular momentum about the axis of emission, and came to the conclusion that it can't otherwise angular momentum wouldn't be conserved since photons can only have +-1 angular momentum. Is a "phonon" a particle that's emitted to conserve angular momentum ( in case the electron has +-2 or 0 angular momentum about an axis) and linear momentum? If a phonon has angular momentum, then how is scattering predicible unless phonons are predicitible?

When you say that it's not the same photon that goes through that gets transmitted in a transparent material, you're not talking about photons which are absorbed and scattered in the same direction as the incident beam right? You're talking about the photons which never get absorbed at all not being the same photons? Do you mean that because photons are bosons some atoms in the excited state will emit a photon to the same state and something later happens with the original photon?

So do I have to understand QED first to understand condensed matter optical conductivity in solids? And any recommendations on a good QED book? All my quantum mechanics consists of the Feynman Lectures Volume 3 - I know almost everything in the book and nothing else: should I read Feynman's QED book?

There was a string here (or was it in the Atomic, molecule, etc. section?) not that long ago regarding phonons. Phonons are the normal modes of lattice vibrations. When light, typically in the visible range, impinge on an object, how transparent it is depends on what modes are available in the material. The vibrational states that are present are the ones that will determine the optical conductivity of the light. It is why optical conductivity is one of the useful technique in determining the phonon spectra in solids. Again, I strongly refer you to a solid state physics text on this.

You do not need to understand QED to understand condensed matter. You do need to understand basic solid state physics (an undergraduate level subject) to go on to do condensed matter (a graduate level subject). A foundation in QFT is also useful to do condensed matter so that you understand the perturbation expansion and all those feynman diagrams that are prevalent in condensed matter.

Zz.