Applications of Quantum Mechanics

Over at the theoretical physics beach party, Moshe is talking about teaching quantum mechanics, specifically an elective course for upper-level undergraduates. He’s looking for some suggestions of special topics:

The course it titled “Applications of quantum mechanics”, and is covering the second half of the text by David Griffiths, whose textbooks I find to be uniformly excellent. A more accurate description of the material would be approximation methods for solving the Schrodinger equation. Not uncommonly in the physics curriculum, when the math becomes more demanding the physics tends to take a back seat, so we are going to spend quite a bit of the time on what is essentially a course in differential equations, using WKB approximations and perturbation theory and what not. To counter that, I am looking for short and sweet applications of quantum mechanics. Short topics which can be taught in an hour or less, and involve some cool concepts in addition to practicing the new mathematical techniques.

I’m hampered in this by not knowing what’s in the second half of Griffiths (the analogous class at Williams was taught out of Park’s book, because he’s there; I used to have a copy of Griffiths in my office, but it seems to have wandered off). I’m currently teaching a much lower-level version of a similar course, though, so I can suggest a few things:

The “Applications” portion of the class I’m currently teaching is really a mad sprint through whatever QM-related topics I can fit into the last three weeks or so. A couple of these, scaled up appropriately, might work.

One obvious application is solid state physics. It’s relatively easy to sketch out the basic ideas that lead to band structure in solids. The full solution is a bit beyond an undergrad course, but you can do the Kronig-Penney model pretty easily. That works well to show how periodic arrays of potential wells gives you bands of allowed states, with gaps between them. The basic idea of band structure is enough to explain a bunch of useful technology– diodes, transistors, LED’s, etc.

Another area is nuclear physics. I don’t do it in the sophomore-level class that I teach, but you can do a remarkably good job of calculating half-lives of radioactive elements using alpha particle tunneling as a model. Somewhere, I have a Mathematica notebook with code to numerically solve the Schrödinger equation for a bunch of different nuclei, which does a great job of getting the decay rates, and the trend with atomic number.

Those two might very well be in Griffiths already, though. A couple other things come to mind as possible topics, though:

If you’re talking about perturbation theory and approximations, you ought to be able to do the Fermi Golden Rule for transitions between atomic states driven by an oscillating electromagnetic field. From there, you can go for the “lies your teachers taught you” topic of demonstrating that you don’t need photons to explain the photoelectric effect. The model is spelled out in a paper by Mandel in the 60’s (I don’t have the cite here, but I can find it if people want to see it), and doesn’t require anything beyond basic perturbation theory.

If the class includes state-vector notation, you can do the No-Cloning Theorem pretty easily (it’s remarkably simple). That’s a good way of getting into all sorts of fun quantum information topics: teleportation, quantum cryptography, some basic quantum computing, etc.

Several commenters to the original post suggested the Quantum Zeno Effect, which is another good one if you’ve done state vectors. Projective measurement is fun stuff.

It’s also relatively easy to get into a lot of cool quantum optics material– the Hanbury Brown and Twiss experiment can be explained in a very straightforward way, and you can actually calculate the relevant correlation functions for a bunch of different cases. And that gets you to the basic techniques that are used for everything in quantum optics.

That’s what I come up with off the top of my head, without knowing the textbook in question. What did I miss?