Being the physics department executive officer (on top of being a quantum physicist) makes me think a lot about our physics college program. It is exciting. We start with mechanics, and then go to electromagnetism (E&M) and relativity, then to quantum and statistical mechanics, and then to advanced mathematical methods, analytical mechanics and more E&M. The dessert is usually field theory, astrophysics and advanced lab. You can take some advanced courses, introducing condensed matter, quantum computation, particle theory, AMO, general relativity, nuclear physics, etc. By the time we are done with college, we definitely feel like we know a lot.
But in the end of all that, what do we know about modern physics? Certainly we all took a class called ‘modern physics’. Or should I say ‘”modern” physics’? Because, I’m guessing, the modern physics class heavily featured the Stern-Gerlach experiment (1922) and mentions of De-Broglie, Bohr, and Dirac quite often. Don’t get me wrong: great physics, and essential. But modern?
So what would be modern physics? What should we teach that does not predate 1960? By far the biggest development in my neck of the woods is easy access to computing power. Even I can run simulations for a Schroedinger equation (SE) with hundreds of sites and constantly driven. Even I can diagonalize a gigantic matrix that corresponds to a Mott-Hubbard model of 15 or maybe even 20 particles. What’s more, new approximate algorithms capture the many-body quantum dynamics, and ground states of chains with 100s of sites. These are the DMRG (density matrix renormalization group) and MPS (matrix product states) (see https://arxiv.org/abs/cond-mat/0409292 for a review of DMRG, and https://arxiv.org/pdf/1008.3477.pdf for a review of MPS, both by the inspiring Uli Schollwoeck).
Should we teach that? Isn’t it complicated? Yes and no. Respectively – not simultaneously. We should absolutely teach it. And no – it is really not complicated. That’s the point – it is simpler than Schroedinger’s equation! How do we teach it? I am not sure yet, but certainly there is a junior level time slot for computational quantum mechanics somewhere.
What else? Once we think about it, the flood gates open. Condensed matter just gave us a whole new paradigm for semi-conductors: topological insulators. Definitely need to teach that – and it is pure 21st century! Tough? Not at all, just solving SE on a lattice. Not tough? Well, maybe not trivial, but is it any tougher than finding the orbitals of Hydrogen? (at the risk of giving you nightmares, remember Laguerre polynomials? Oh – right – you won’t get any nightmares, because, most likely, you don’t remember!)
With that let me take a shot at the standard way that quantum mechanics is taught. Roughly a quantum class goes like this: wave-matter duality; SE; free particle; box; harmonic oscillator, spin, angular momentum, hydrogen atom. This is a good program for atomic physics, and possibly field theory. But by and large, this is the quantum mechanics of vacuum. What about quantum mechanics of matter? Is Feynman path integral really more important than electron waves in solids? All physics is beautiful. But can’t Feynman wait while we teach tight binding models?
And I’ll stop here, before I get started on hand-on labs, as well as the fragmented nature of our programs.
Question to you all out there: Suppose we go and modernize (no quotes) our physics program. What should we add? What should we take away? And we all agree – all physics is Beautiful! I’m sure I have my blind spots, so please comment!