Is there a guiding principle to determine when quantization is needed when modeling EM-matter interactions?

Question

I'm an undergrad engineering student and I need some guidance to help me understand a few issues regarding classical electromagnetism (EM).

I'm interested in engineering applications where there is an interaction between EM and matter (e.g., microfluidics technology, electrokinetic phenomena, magnetic resonance technology, plasma technology, etc).

Based on my readings so far, it appears that many applications of EM-matter interactions can't be fully understood or modeled without at least some quantum mechanics. I'm increasingly finding myself unable to predict if a certain EM-matter interaction can be modeled using only classical EM, or if quantum mechanics is needed.

Some would say classical EM is valid as long as "too small/too fast" conditions are avoided. But this doesn't really help much. Even common everyday phenomena such as an EM radiation passing or reflecting from matter can't be fully understood without some quantum mechanics. I presume they may respond by indicating that this is actually a molecular-scale phenomenon, since the radiation is interacting with the molecule itself. However, by this reasoning, everything would require quantum modeling, even the molecules of my hand pushing against the molecules of a door knob, since it is a molecular-scale interaction.

To summarize:

1. How come many engineering EM books spend so much time describing all sorts of EM-matter interactions without any mention of QM? (e.g., propagation of EM waves through matter (i.e., conductors, dielectrics), reflection of EM waves from matter, etc). Why is a classical modeling sufficient for such EM-matter interactions?

2. How can I predict if quantum mechanics is needed for a particular application involving EM-matter interactions? (P.S. I'm aware of the "too small/too fast" rule of thumb. Please see the last paragraph in my post).

Edit: A few clarifications:

• I'm not asking about field quantization (i.e. QED/second quantization). I'm only focusing on quantization of electrons.

• I was mainly looking for a guiding principle that allows me to predict when quantization is needed. Or is it the case that there are no such principles and I simply have to recall a list of exceptions to classical EM (as in UVphoton's reply)?

Thank you for your help!

Answer 1

There’s a couple of ways to to answer the question. The short answer is that often the classical theory is quite good and does the job.

Consider light. The emission, absorption, energy of the photon, spontaneous emission and stimulated emission are all inherently quantum mechanical. But for optical problems, those processes are sometimes not that important, until they become important.

Geometric Optic you can use ray theory. That will give you an idea of the focus, aberrations magnification etc. and is fine for some problems.

If you want the intensity, you might need to consider the polarization of each ray as it is reflected or refracted.

If the object is small or a sharp edge or if the light is coherent then you need wave theory for diffraction and interference.

And with those tools you can solve a lot of problems. But then there are other problems, like light interacting with a atom, or a molecule, or structures where electrons are confined and have discrete energy levels, the quantum becomes very important again. So in addition to geometric optics, or wave optics, you also have quantum optics or quantum statistics of light.

Even though Lasers are truly “quantum” I would argue a lot of lasers get engineered, built and used without people thing of the quantum…. Until they need a special wavelength or a special entangled photons source or some other specialty purpose.

In electrical engineering and device physics, electrons moving through the lattice is quantum all the way. But once you have a band structure for the semiconductor and you have an effective mass for an electron and an effective mass for a hole. You can start to think about them as individual particles acted on by electric fields and and instead of the quantum mechanics of scattering, it gets reduced to a mobility that depends on the average time the electrons have between collisions. And that is great for designing pn junctions and some kinds of transistors, but if you want to design a diode laser or an efficient LED you may dive back into the quantum again because you are growing thin layers of materials where the electrons are only allowed discrete energies (quantum wells). Or you might want to work with an new material like graphene or a disulfide where your device is constructed with a single layer of atoms and the quantum will be important again.

Also, physicists, chemists, electrical engineers tend to look and analyze the world with a slightly different vocabulary and math depending on their training and what they are studying. This also impacts how they teach their material to students.

So long answer, but the quantum is there underneath it all….

Answer 2

To add just a little to UVphoton's detailed answer:

The non-quantum, "classical" approach to EM & its interactions with matter yields entirely satisfactory engineering results when the wavelengths involved are ~several orders of magnitude greater than the dimensions of an atom, which is where QM effects begin to get important.

They also yield satisfactory engineering results when the number of matter particles involved in the interaction are of order ~billions or greater, rather than ~tens of thousands or less (quantum clusters, quantum dots, etc.) which is where quantum effects start being apparent.