Teaching Quantum Mechanics to "Liberal Arts" Students

Apr 11 2011 Published by under Academia, Astronomy & Physics, Quest University Canada

Before I even get started, I have to get defensive about the "scare quotes" around "Liberal Arts" in the title. The word "Liberal Arts" students is used to mean a lot of different things. The context I'm using it in here could very easily be interpreted as the context that I most dislike, hence the scare quotes. Often, when science types talk about "liberal arts" students, there is a subtext of "people who can't handle math and science"... that is, somebody who, at least as far as the study of science goes, is a lesser. That's not what I'm talking about here. I'm talking about "liberal arts" students as in the vast majority of students who are at higher end colleges and universities in North America. Students who aren't getting a technical degree, whose studies aren't "training", but who are studying a broad range of topics with the goal of becoming broadly educated. Yes, even many/most physics majors are "liberal arts" students, because they do things other than just pure physics. Even some engineering majors are this!

At Quest University, students in their first two years take (for the most part) classes that are part of a "Foundation Program". There are 16 of these classes, five of which are science courses (which I think is pretty impressive, if you compare the ratio of science that shows up at most places). One of these is "Energy & Matter". This course has never been extremely well-defined, and indeed each time it's been taught it's been a different course, but at its core is the course in the Foundation that introduces students to physical science at the fundamental level. (Another meta-course, "Earth, Oceans, and Space", is about the "larger systems" applications of physical science.) Thus, it's been taught as standard introductory chemistry course, among various other ways. The last time I taught it, I tried to go for my own ideas as to what the most important things to get out of a course with that title would be. The result was mostly physics, with some chemistry mixed in.

More recently, some of us have been trying to make it so that students will have some idea what this course will be when they sign up for a given iteration of it. As such, we've taken to subtitling the course. A colleague of mine will be teaching it entirely as a lab course. Another (if he ends up full-time at Quest) will teach it focusing around understanding the energy needs and uses of a realistic city. One constraint we always have is that there is a huge range of abilities in this class. Some people have a strong background in physics, some people can barely do algebra (like all too many college students). In order to not bore the stronger students without blowing away the students with weaker backgrounds, one tactic is to teach something that you know that none of them will have had in high school. To that end, I've created the course "Energy & Matter: Our Quantum World", which tries to really get into the meat of quantum mechanics, but at the level approachable by a student who has had no previous physics nor any calculus.

Although I still need to tune it up, I think it worked. The thing about this class is that I wanted it to go beyond the descriptive level that you do often see in non-majors general physics courses. I wanted students to struggle quantitatively with the notion of probabilistic reality, with calculating amplitudes and probabilities. The result was that this time around, I spent much of the course focused on electron spin and thought-experiments based off of the Stern-Gerlach Experiment. Towards the end, we got to talking about quantized energy levels in general, and the Hydrogen atom in particular. We also talked about fermions and bosons, and the notion of a "Fermi gas" (including the electrons in a conductor). I did give them the Schrödinger Equation, but only in its most abstract form:

\(\hat{H}\left|\psi\right>\ =\ E\,\left|\psi\right>\)

Since I wasn't using calculus, I wasn't able to give them the full differential form for the kinetic energy part of the Hamiltonian. Then again, the notion of coping with mathematical abstractions was a major theme of the course. Some of the material I covered is stuff that physics students may not see until a junior year quantum mechanics class: Dirac notation, propagating amplitudes, Dirac spinors, matrix representation of angular momentum operators. This did mean I had to teach a wee bit of matrix multiplication to the students in the class, but it was all quite approachable.

Although there are definitely things I will tune up next time around— I'd like to figure out a way to actually talk about waves so that the term "wave function" can be more than jargon, if I can figure out how to make it fit without making the class overfull— I believe that overall the effort was successful. It was quite a marathon for me, as I was effectively writing the textbook as I taught the class. (I would joke that I would write the reading assignment in Google Docs, and the students would watch as a typed it. It wasn't quite that bad; for one, I used LaTeX, and for two, all but two or three days I had the next day's reading assignment posted before the beginning of the current day's class....) There were a few students who felt quite lost, but frankly, that was as a result of a particularly weak grounding in algebra, and they would have had trouble in my previous iteration of Energy & Matter. Many students, however, seemed to get it, and really seemed to grasp what was going on with these probabilistic systems. A few students also commented on how cool they thought it was. My favorite quote was from a student at the end of her presentation about the Quantum Zeno effect: "Quantum mechanics is something that's hard for us to conceptualize, but it's also very very awesome."

2 responses so far

  • Ulrich says:

    Hi Rob,

    My book The World According to Quantum Mechanics: Why the Laws of Physics Make Perfect Sense After All might be useful for your project. You can get a fairly good idea about the content from my website This Quantum World (which however lacks the math) or from the publisher's website. The Preface, Contents, and Chapter 1 can be downloaded from there (for free).

    Best wishes,
    Ulrich

  • william e emba says:

    You are familiar with Thomas Jordan Quantum Mechanics in Simple Matrix Form? Now a Dover paperback, it's mostly done with 2x2 matrics.