### Physics Curriculum: Quantum Mechanics

My reply in Chad Orzel's blog, reproduced here in my own blog with additional comments, remarked that my "freshman" quantum mechanics class had served to develop (in me, at least) an intuitive view of how non-relativistic quantum mechanics works. [Actually, I'm pretty sure it had a similar effect on at least two other people in that class who went on to PhD degrees in theoretical physics and chemistry.] I am posting more about this based on a request in the comments. Sorry for the delay, but I did not have time to work on my initial draft at all this week. I'm still not sure it covers all of the key points, but it is a starting point for discussion.

I'll mention above the fold that one reason I think quantum mechanics is in more need of "reform" than instruction in classical mechanics is simply the fact that it is comparatively young. There are perfectly serviceable bridges in use that are over a hundred years old, designed with the same principles of static equilibrium we teach today. That physics, and how to communicate it to students, was already on pretty solid ground maybe a half century before quantum mechanics was discovered, let alone taught! In contrast, we are only a few generations removed from the very first graduate courses in quantum mechanics and it is unclear to me how much those have changed since, say, 1935. (I'd say we are only on the second generation of graduate level textbooks, if that.) Certainly most undergrad treatments of quantum mechanics use the quasi-historical approach, following the totally wrong ideas of Bohr so QM can be evolved from the familiar territory of classical mechanics.

There were many differences between my course and the normal curriculum at a typical university or college even today, more than a quarter century later.

This was not a "modern physics" class, the third semester of physics as codified in typical University Physics textbooks. Not even close. First, relativity had been dealt with a year earlier, in the mechanics course. It did not appear at all to distract anyone from the primary point of the course. Second, the only phenomenology was that of atomic physics. There was none of the "stamp collecting" of different topics from atomic, condensed matter, nuclear, or particle physics. It was a quantum mechanics class. Period. Hence my suggestion that Chad think about a class that uses his AMO research for examples without trying to teach three or four PhD subject areas with only a few weeks devoted to each. Teach one thing, and teach it well.

The textbook was the 4th book in the 5-part Berkeley Physics Course. Most students in the class had come through that sequence, which assumed that you had completed calculus 1, 2, and 3 by the third quarter of your freshman year and were currently enrolled in a differential equation course when starting mechanics. Others were 3rd year students who had wandered in from the regular sequence taught from the original edition of Halliday and Resnick. The prerequisite course, from the "waves" book (still possibly the best book on the topic, period), meant it was assumed that everyone could solve the basic PDE for waves and could do the vector integrals encountered in E&M.

The instructor was a professor of physics with two PhD degrees, one in physics and the other in philosophy. He taught some courses on the philosophy of science in addition to courses in physics. Some years later I came to realize that important parts of his approach to the course followed the Feynman Lectures (which might have been the text for this sequence in earlier years) as well as being colored by his own research interest in conscious observation vis-a-vis objective reality (EPR, etc) from the philosophy side of his career.

A key element in the course was to break down our existing physical intuition. This was the part that seemed heavily influenced by Feynman's lectures on quantum mechanics, although it also built on what we could do with electromagnetic waves. The basic point he made was that everything we knew was wrong. We knew how to do orbits with the coulomb force. We knew how an accelerated particle would produce dipole radiation. We knew how to calculate the energy carried off, and hence we could prove that hydrogen atoms do not exist. Oops. Ditto for several other things, at various points in the course. The philosophical point was not just that our knowledge of mechanics was incomplete, it was that it was wrong. Fundamentally wrong. It could not be trusted.

From the other direction, if you start with classical non-relativistic quantum mechanics, your results can be trusted. You can derive classical mechanics from quantum mechanics, but not the other way around. (That is, Bohr was totally wrong in his approach.) Quantum mechanics tells you when classical mechanics can be trusted, and when it can't. There was no formal emphasis on Dirac's proof of the connection, but this was no surprise to me when I encountered it. The point of emphasis was quite practical: the questions that quantum mechanics, and only quantum mechanics, can get right.

But it could have been something more subtle that made the class work for me. There was none of the "quantum weirdness" that was so common at the time and still appears in textbooks that start from the Bohr model. The only weird effects were ones like Feynman's bullets fired at slits in armor on a battleship, the ones that modern EPR experiments have documented repeatedly. There was no emphasis on totally wrong ideas like the need for a quantum jump in the Bohr model. We had overlap integrals between wave functions that made it quite clear that transitions were entirely local.

The one thing it did not have (IIRC) was much in the way of linear algebra built on photon polarization as a model example, the starting point for my graduate course, where the fact that QM is actually an algebra acquired greater relevance. I have, however, seen this starting point used with great success in a senior QM course taught at another university I have been around and would recommend it.

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