I got way behind on my reports from my Modern Physics class– the last one was over month ago, and the class has since ended. There’s enough material left to be really awkward as a single post, though, so I’m going to take my cue from Brandon Sanderson and split it into three parts.
The remaining material is from the sprint-to-the-end “Applications of Quantum Mechanics” portion of the class, and breaks into three roughly equal chunks. The first of these is dealing with atomic and molecular physics.
Class 22 presents the full quantum model of Hydrogen, starting from the Schrödinger equation in spherical coordinates. One of the first times I taught this class, I wrote that up on the board, and the students just goggled at me. “This is a joke, right?,” one of them asked.
It’s not a joke, though it is a horrible-looking mess. I put it down mostly for cultural purposes, so they’ve seen it at least once, but we don’t really do much with it. (Beyond explaining that the physics convention for naming the polar angles is the reverse of the math convention– theta is phi, and phi, theta). I sketch out the idea of separation of variables, which breaks it into more tractable pieces, and then give the solutions in terms of spherical harmonics and named polynomials. This introduces the n, l, m quantum numbers for the energy levels, and I talk a bit about how to identify those.
Class 23 picks up from the very brief discussion of angular momentum at the end of the previous class, and introduces the Zeeman Effect as proof of the existence of the degenerate sublevels created by all those angular momentum states. This is done entirely through semi-classical arguments about orbiting electrons acting like current loops, and so on.
I then say that this explains almost all of the observed transitions in hydrogen, with the exception of the tremendously important 21-cm line. I explain how this can’t be explained as a transition between closely separated Rydberg levels, because the transition is seen in cold clouds of interstellar gas, but it must be some low-lying state resulting from new physics.
This is a lead-in to the Stern-Gerlach experiment, and the notion of electron spin. I then explain the hyperfine splitting is very vague and semi-classical terms (the spin of the proton in the nucleus creates a weak magnetic field that interacts with the spin of the electron to produce two closely spaced energy levels), and say that the addition of spin allows quantum mechanics to explain all of the observed energy levels in hydrogen (which isn’t quite right, because of the Lamb shift, but it’s close enough for government work).
Class 24 moves on to multi-electron atoms, and a whirlwind tour of degeneracy-breaking effects– electrostatic shifts, spin-orbit coupling, the hyperfine interaction. These are pretty much just named, with a tiny sketch of how they work. I also talk about Pauli Exclusion, and how it leads to chemistry.
Showing my own biases, I then talked for a little bit about Rydberg atoms, and how they can look very much like the original Bohr model states. I throw in a few things about cool applications of Rydbergs, from terahertz radiation detectors to cold plasmas.
Finally, I talk a bit about interactions between atoms, and how they can be understood in terms of little dipoles that are either aligned or opposed, giving you either attractive or repulsive interactions. This lets you qualitatively understand the sort of molecular potentials you draw in the Born-Oppenheimer approximation, and sets the stage for solid state.
These three classes are ordered in a way that I think provides a reasonable narrative flow through all of these topics (it borrows heavily from the Six Ideas books in places). This is not, however, the way that the textbook we were actually using does it, leading to a lot of section-skipping and jumping around. Which is a little inconvenient, but not nearly as bad as it gets later.