B Interaction of light with atoms

[jeremyfiennes]

TL;DR Summary

Interaction of light with atoms. Two ways of describing.

One description of the interaction light with atoms states "Light waves incident on a material induce small oscillations in the atoms, causing each to radiate a small secondary wave in all directions". And another that "A photon with the right energy causes an electron to jump up to the next higher energy level, eventually dropping back to the lower state with the emission of a photon". How do these two relate?

 

[vanhees71]

Both descriptions are correct and refer to different levels of description. The first one considers the interaction of a classical electromagnetic field with quantized atoms (i.e., a nucleus surrounded by electrons, where the nucleus often is entering the description just through its static electromagnetic field only). This is an approximation, but you get amazingly far with it. E.g., contrary to many textbooks the photoeffect as well as the Compton effect can be described in this socalled "semiclassical approximation".

The second description refers to the fully quantized theory, quantum electrodynamics, i.e., all physical objects, i.e., the electrons, atomic nucleus, and the electromagnetic field. This is the hitherto most comprehensive description, valid for everything observed on atoms today.

The most simple reason, why one needs to quantize the electromagnetic field is spontaneous emission. This describes the fact that if you have a single atom with no other electromagnetic field than that of the nucleus and the electrons (i.e., no em. waves present) and the atom is not in its ground state, sooner or later the atom relaxes to lower states and finally to the ground state emitting one or more photons spontaneously.

 

[jeremyfiennes]

Thanks. My problem is with reflection/refraction. On the semi-classical model the atoms can vibrate at any frequency, and re-emit at that same frequency. On the qm model the emitted frequency is that corresponding to the difference in the two energy levels.

 

[jambaugh]

The first is a classical description of the phenomenon. It treats the atom as a collection of point charges. The second is a quantum description. Let's begin by pointing out that we are describing phenomena. A phenomenological description says something like "when this happens then that will happen." Phenomenologically both describe how light, electromagnetic radiation interacts with an atom.

The classical description is an ontological description describing the atom and its components as objects with objective states and similarly the light as a classical object, a field with an objective state of reality. If you replace the atom with a large scale collection of charged objects and consider strong electromagnetic fields then it is perfectly valid description for the general behavior. It however was found insufficient to describe very small scale interactions and phenomena such as the photo-electric effect and quantized emission spectra for atoms.

The quantum description is more purely phenomenological. While we speak of "a photon" as if it were and objective particle, it is important to understand that the language (as understood by a deeper study of quantum theory) is describing a non-objective phenomenon. A photon does not have a "state of reality" in the classical sense even though we often refer to its "state vector". Rather a photon is a phenomenon of transmitted energy and momentum propagating via the electromagnetic field (another phenomenological entity in the quantum description).

We give meaning to these phenomenological descriptive entities by amplifying their effect (and cause) to entities of sufficiently large scale to be properly described again in a classical objective language. In one sense a photon is the phenomenon which causes a photo-multiplier tube to go "click!". The whole science of quantum mechanics then is a logically coherent set of empirically verified principles which describe how such phenomena behave.

While it is perfectly possible to describe classical objects phenomenologically there are certain a priori assumptions about the behavior of classical objects when using a classical description which can be relaxed in the more active description we find in quantum theory. Thus the phenomenological quantum description is richer allowing us to describe more possibilities about the way things may happen. It would also seem, such a description is necessary to understand elementary processes such as light impinging upon an atom.

 

[jeremyfiennes]

While it is perfectly possible to describe classical objects phenomenologically there are certain a priori assumptions about the behavior of classical objects when using a classical description which can be relaxed in the more active description we find in quantum theory. Thus the phenomenological quantum description is richer allowing us to describe more possibilities about the way things may happen. It would also seem, such a description is necessary to understand elementary processes such as light impinging upon an atom.

Thanks. Very erudite! I realize that we are trying to descibe highly complex phenomena, all of whose aspects simple models don't necessarily cover. My basic problem is I think to visualise multi-frequency reflection/-refraction on the quantum energy-level-jump-and-re-emission approach.

 

[forcefield]

My basic problem is I think to visualise multi-frequency reflection/-refraction on the quantum energy-level-jump-and-re-emission approach.

Reflection/refraction happens at all frequencies while absorption/emission only happens at certain discrete frequencies.

 

[jambaugh]

I'll repeat what my thesis advisor said to me. Trying to visualize what's going on is a mistake. (We visualize objects and trap ourselves into object based descriptions.)

You could try using your social intuition rather than visual since we treat personalities conceptually in the same phenomenological way. A photon is a packet of insults thrown by other atoms, when an atom hears them, certain ones are so over the top they tend to be ignored and likewise with weak insults. But one of the right energy will make the atom mad. It then vents its ire shouting out an insult of its own.

 

[jeremyfiennes]

So what is the quantum explanation of reflection at general non-absorption frequencies?

 

[Nugatory]

My basic problem is I think to visualise multi-frequency reflection/-refraction on the quantum energy-level-jump-and-re-emission approach.

That’s not an effective way of thinking about reflection and refraction.
These are phenomena observed when an electromagnetic wave interacts with a chunk of matter (reflective surface or lens). The chunk of matter is composed of a very large number of interacting charged particles; the simple picture of a bound electron that we get from the Schrodinger solution for an isolated hydrogen atom doesn't apply. The electromagnetic wave is a superposition of many different states with different numbers of photons at different energy levels; considering how a single photon is scattered in an interation with a single electron isn't going to be a useful picture.

So what is the quantum explanation of reflection at general non-absorption frequencies?

The B-level answer is "because that's what quantum electrodynamics says happens in this enormously complex problem". Richard Feynman's non-technical book "QED: The strange theory of light and matter" will give you some feel for how quantum electrodynamics produces this result, but of course says nothing about the details of the interaction, which are what you're asking for. To get those details is going to take an A-level answer.

 

[jeremyfiennes]

Ok. Thanks.