# Why Teach “Modern Physics?”

The scare quotes in the title are to distinguish “Modern Physics” classes like the one I’m teaching this term from modern physics as a general subject, which, of course, all right-thinking people should study in depth. The question comes from a comment by Coriolis on last week’s post about what “Modern Physics” is as a class:

Having passed through those classes (I’m now a grad student), I have to say I didn’t see much worth in the Modern physics class (and your description of it is pretty much how I remember it, except without the relativity). It’s basically in that middle ground trying to give you a “taste” of QM, without actually going into the math and subject in a way that makes sense like the first real QM class does. Maybe it somehow helped subconsciously when I took the first QM class, but I don’t think so.

The existence of these classes– a whirlwind tour of (special) relativity and quantum mechanics, and applications thereof– is a little problematic, for exactly the reasons Coriolis notes: there isn’t enough time spent on each topic to really learn it in depth. And, in fact, there are other ways of approaching the same material. I think that sophomore-level “modern physics” courses do serve a couple of purposes, though.

The whole reason for “modern physics” classes at the sophomore level is as a bridge between the intro-level courses in Newtonian mechanics and E&M and the upper-level physics classes. While there are some weird phenomena that crop up in those classes, for the most part, they’re pretty approachable: the physics involved deals with ordinary objects and everyday (or, at least, not ridiculously odd) situations, and the math involved is very straightforward calculus.

When you get to quantum mechanics, though, you need to make two big jumps. One is mathematical– the Schrödinger Equation is a second-order differential equation, the idea of eigenstates and so on brings in a lot of linear algebra, quantum wavefunctions are necessarily complex numbers, etc.– and the other is conceptual. The way things behave in the quantum regime is so utterly unlike the way that things behave in everyday life that it takes a little while to get your head around the whole idea.

“Modern Physics” classes in the sophomore level try to bridge this gap. Many of the students taking them are only just getting to the point in the usual math curriculum where they can begin to understand the techniques involved, so these classes typically try to ease into the relevant topics. I spend a whole class on complex exponentials (because the math department doesn’t), for example, and do a computer exercise in Mathematica to introduce the idea of Fourier series before diving into the uncertainty principle.

At the same time, the classes try to hit most of the essential concepts: the idea that particles need to be described as wave-like in some respects, the idea of energy quantization, some basics of wavefunctions, etc. Students don’t go through all the gory details of calculating wavefunctions in real situations, but they get some of the flavor.

The idea of sophomore-level “modern physics” is to let students see a little of both the mathematics and the concepts before they get to the real deal, so that they’re not doubly blown away when they hit “real” quantum mechanics. If you just throw students into a regular quantum class with no preparation, they go into vapor lock– they can’t handle the math, they don’t understand the concepts, and they shut down. By giving them half of the math, and half of the concepts in advance, they’ve got a little something to cling to when they hit “real” quantum mechanics.

There are, of course, other ways to do this. When I was an undergrad at Williams, the third course in the physics sequence, in the spring semester of the sophomore year, was called “Waves and Optics,” but was really a stealth math methods course. It introduced all the key mathematical concepts for quantum mechanics, in a more familiar context. We talked about waves on strings, and used that to introduce wave equations and Fourier analysis. We talked about physical optics, and used that to introduce a little complex analysis, representing light waves as the real part of a complex exponential. We talked about normal modes of oscillators, and used that to set up ideas about basis states, and so on.

I thought that approach worked very well as a way of setting up the math needed for quantum physics in an approachable way. The topics covered had fairly direct and comprehensible applications, so there was relatively little conceptual oddness, leaving time to get our heads around the math. Then, in the quantum class, we could deal with all the gory details a little more easily. It also fit well with the research interests of the faculty at that time, who were very heavily biased toward lasers and optics in general.

There’s another purpose served by the “modern physics” class, though, which is to give students who won’t necessarily go on to take all the upper-level electives (or who won’t be able to, due to limited resources for teaching electives) some idea of the key ideas of modern physics. At Union, we generally manage to offer one or two upper-level electives per year– classes like “Particle and Nuclear Physics,” “Statistical Mechanics,” “Modern Physical Optics,” “Solid State Physics” and the like. That means that students following the normal course sequenceget a shot at maybe three of these. We require only one for graduation with a Physics major.

A full-blown quantum mechanics class doesn’t have time to really get to any of the key applications– if you’re starting with the basic postulates, you just don’t have time to get through all the solvable problems and all the solution techniques in time to get to the details of band structure and its implications for solid state physics. That’s why the special topics classes exist, after all.

That means that, in the absence of something like a “modern physics” class, students could graduate with a major in physics without ever studying some of the topics that are most closely associated with physics. The end-of-term sprint through applications of quantum mechanics does at least give students a glimpse of these topics– I spend a couple of classes on band structure, and how diodes and transistors work, for example, and a couple more on basics of nuclear physics and nuclear decays. That way, they have at least a glimmer of an idea of what “beta decay” means, down the line, whether they get the chance to take “Solid State Physics,” or “Particle and Nuclear Physics” down the line, or not.

The calculation of costs versus benefits of this approach comes out differently for different departments. There are trade-offs involved in either approach– what Williams did, back in the day, did a fine job of preparing us for quantum mechanics, atomic physics, or laser physics, but in the time I was there, the department never offered any classes on particle or nuclear physics (and thus, my knowledge of those areas remains pretty sketchy). That worked fine for them, as all the experimental faculty did work in those areas, but the same approach wouldn’t work at Union, where we have faculty doing research in a wider range of areas.

I do have some doubts about the utility of the “modern physics” approach, and as a result, I tend to push the “stealth math methods class” aspect of the course a little harder than may be typical. I don’t think they can be dismissed out of hand, though– they do play a useful role in the curriculum, which is why they’re common enough to have spawned a whole category of ridiculously expensive textbooks.