Michael Nielsen’s recent essay “Why the world needs quantum mechanics,” about the quintessential weirdness of quantum phenomena, provoked Dave Bacon to ask if there’s a better way to teach introductory courses in quantum physics. This question strikes a chord with me, since my first semester of college quantum — the class known as “8.04” — was rather remarkably dreadful.
It began with some fluff about early models of the atom, leaving out most of the ideas actually proposed in favor of a “textbook cardboard” version of the discoveries made in early TwenCen. If we can’t teach history well, why teach it at all? We’re certainly not promoting a genuine understanding of how science works if we only present a caricature of it. I doubt one could even instil an appreciation for the problems which Bohr, Heisenberg, Schrödinger and company solved in the years leading up to 1927: sophomore physics students can’t follow in their footsteps, because sophomore physics students don’t know as much classical physics as professional physicists of the 1920s did. To understand their starting point and the steps they took requires, oddly enough, subject material which even MIT undergrads don’t learn until later.
After the textbook-cardboard version of history, we proceeded to solve the Schrödinger Equation in a great many different circumstances. This was supposed to “build intuition about quantum mechanics,” but I think all it built in most people was a loathing of differential equations. The course was capped off with a cursory treatment of the Bell Inequality.
Looking back, the only thing I learned in 8.04 which I didn’t see derived again, more cleanly and more memorably, in a later course was how a delta-function potential acts in the Schrödinger Equation — and that takes, what, half the back of an envelope to work out? (OK, given small handwriting.)
I have occasionally wondered whether it would be possible to build a first-term quantum physics course out of Feynman’s QED: The Strange Theory of Light and Matter (1985). If you’re teaching to university students, they probably already have experience with complex numbers, trigonometry and some amount of calculus, so you’ll be able to write actual exercises based on the book’s conceptual material.
Either before or after the chapter on the Standard Model’s particle content, expand the book with two-state systems, the Bell Inequality and entanglement stuff. (I might do it after the Standard Model chapter, so I could lead into it with a little kaon physics.) After entanglement, introduce decoherence. Follow with the model of electrons hopping from atom to atom expounded in the Lectures on Physics, chapter III-13, and use it to motivate band-gap behavior and, by shrinking the lattice spacing, the SchrÃ¶dinger Equation (chapter III-16). Solve the particle-in-a-box and the harmonic oscillator, and then bid the kids a happy summer vacation.
I don’t pretend to know how well this programme would work, and I’ve certainly never tried it on a live audience, but I do think the way I was introduced to QM was wasted effort which fails in its stated aim of “building intuition.” The time is nigh for reform — come, let us tear down the old edifice of incomprehensible authority and build a better one anew! (Singing “Dem Bones” is optional.)