Some of my colleagues and I have started an interesting discussion about how to teach quantum theory to undergraduates. We have courses in the second, third, and fourth years. The three courses have independently evolved, depending on who teaches each. Some material gets repeated and other "important" topics get left out. One concern is that students seem to not "learn" what is in the curriculum for the previous year. The goal is to have a cohesive curriculum. This might be facilitated by using the same text for both the second and third-year courses.

This has stimulated me to raise some questions and give my tentative answers. I hope the post will stimulate lots of comments.

The problem that students don’t seem to learn what they should have in pre-requisite courses is true not just for quantum. I encounter second-year students who can’t do calculus and fourth-year (honours) students who can’t sketch a graph of a function or put numbers in a formula and get the correct answer with meaningful units. As I have argued

before, basic skills are more important than detailed technical knowledge of specific subjects. Such skills include relating theory to experiment and making order of magnitude estimates.

Yet, given the following should we be surprised?

At UQ typical lecture attendance probably runs at 30-50 per cent for most courses. About five per cent watch the video. [University policy is that all lectures are automatically recorded]. The rest are going to watch it next week… Only about 25 per cent of the total enrolment in my second-year class are engaged enough to be using clickers in lectures. Exams are arguably relatively easy, similar to previous years, usually involve choosing questions/topics, and a mark of only 40-50 per cent is required to pass the course.

I do not think curriculum reform is going to solve this problem.

Having the same textbook for 2nd and 3rd year does have advantages. This is what we do for PHYS2020 Thermodynamics and PHYS3030 Statistical Mechanics. But, some second years do struggle with it... which is not necessarily a bad thing. The book is

Introduction to Thermal Physics, by Schroeder.
Another question is what approach do you take for quantum: Schrodinger or Heisenberg, i.e. wave or matrix mechanics? The mathematics of the former is differential equations, that of the latter is linear algebra. Obviously, at some point you teach both, but what do you start with. It is interesting that the Feynman lectures really start with and develop the matrix approach, beating the two level system to death...

At what point do you solve the harmonic oscillator with creation and annihilation operators?

When do you introduce Dirac notation?

I would be hesitant about using Dirac notation throughout the second year course. I think this is too abstract for many of our current students. They also need to learn and master basic ideas/techniques about wave mechanics: particle in a box, hydrogen atom, atomic orbitals, … and connecting theory to experiment... and orders of magnitude estimates for quantum phenomena.

What might be a good text to use?

Twenty years ago (wow!) I taught second (?) year quantum at UNSW. The

text I used is by Sara McMurry. It is very well written. I would still recommend it as it has a good mix of experiment and theory, old and new topics, wave and matrix mechanics….

It also had some nice computer simulations. But it is out of print, which really surprises and disappoints me.

Related to this there is

a discussion on a Caltech blog about what topics should be in undergraduate courses on modern physics. Currently, most "modern" physics courses actually cover few discoveries beyond about 1930! Thus, what topics should be added? To do this one has to cut out some topics. People may find the discussion interesting (or frustrating…). I disagree with most of the discussion, even find it a little bizarre. Many of the comments seem to be from people pushing their own current research topic. For example, I know it is Caltech, but including density matrix renormalisation group (DMRG), does seem a little advanced and specialised...

There is no discussion of one of the great triumphs of "modern" physics, biophysics!

I actually think every undergraduate should take a course in it.
What do you cut out?

I actually think the more the better, if the result is covering a few topics in a greater depth that develops skills, creates a greater understanding of foundations, that all leads to a greater love of the subject and a desire and ability to learn more.

In teaching fourth year condensed matter [roughly Ashcroft and Mermin] it is always a struggle to cut stuff out. Sometimes we don't even talk about semiconductor devices. This year I cut out transport theory and the Boltzmann equation so we could have more time for superconductivity. This is all debatable... But I hope that the students learned enough so that they if they need to they have the background they need to easily learn these topics.

A key issue that will divide people concerns the ultimate goal of a physics undergraduate education. Here are three extreme views.

A. It should prepare people to do a PhD with the instructor.

Thus all the background knowledge needed should be covered, including the relevant specialised and advanced topics.

B. It should prepare people to do a physics PhD (usually in theory) at one of the best institutions in the world.

Thus, everyone should have a curriculum like Caltech.

C. It should give a general education that students will enjoy and will develop skills and knowledge that may be helpful when they become high school teachers or software engineers.

What about Academic Freedom?

This means different things to different people. In some ways I think that the teacher should have a lot of freedom to add and subtract topics, to pitch the course at the level they want, and to choose the text. I don't think department chairs or colleagues should be telling them what they "have" to do. Obviously, teachers need to listen to others and take their views into account, particularly if they are more experienced. But people should be given the freedom to make mistakes. There are risks. But I think they are worth them in order to maintain faculty morale, foster creativity, maintaining standards, and honouring the important tradition of academic freedom. Furthermore, it is very important that faculty are not told by administrators, parents, or politicians what they should or should not be doing. Here, we should bear a thought for our colleagues in the humanities and social sciences,

particularly in the USA, who are under increasing pressure to act in certain ways.

I welcome comments on any of the above.

My colleagues would particularly like to hear any text recommendations. Books by Griffiths, Shankar, Sakurai, and Townsend have been mentioned as possibilities.