Teaching advanced quantum mechanics

[Scott Hill]

I'm teaching advanced undergraduate quantum mechanics in the spring for the first time, using Griffiths' Introduction to Quantum Mechanics. (It's basically "mathematical methods of quantum mechanics: eigenstates, bra-ket notation, ladder operators, WKB approximation, etc). If you've taken or taught this class, I'd like to know how it was done and how well it worked.

The class is heavy on the derivations, and a straight-up lecture isn't going to be very helpful, because there are few things more boring or less useful than watching someone else do algebra. Enrollment is currently small (4 students), so I would like them to present derivations in class, under my watchful eye. (It might be the first time I ever grade students on "participation", which will be interesting too.)

What have y'all seen and/or done? General thoughts about teaching advanced heavy-on-the-derivations classes are welcome too.

 

[DrClaude]

What QM will they have already seen? If you pardon me being blunt, Griffiths is a bit light for an advanced course.

 

[Scott Hill]

What QM will they have already seen? If you pardon me being blunt, Griffiths is a bit light for an advanced course.

They've had a one-year Modern Physics course out of Krane.

 

[Herman Trivilino]

In my opinion, if you want students to understand derivations the worst way to do it is to have the instructor spend time doing derivations on the board. Better ways include assigning them as reading and then making students answer questions about them.

Check out this resource: http://physics.oregonstate.edu/~mcintyre/ph425/spins/index_SPINS_OSP.html

Even if you don't adopt McIntyre's textbook, you can get a lot good ideas from it and the other resources. You will want to play with the software and consider having your students use it.

 

[Andy Resnick]

I'm teaching advanced undergraduate quantum mechanics in the spring for the first time, using Griffiths' Introduction to Quantum Mechanics. (It's basically "mathematical methods of quantum mechanics: eigenstates, bra-ket notation, ladder operators, WKB approximation, etc). If you've taken or taught this class, I'd like to know how it was done and how well it worked.

The class is heavy on the derivations, and a straight-up lecture isn't going to be very helpful, because there are few things more boring or less useful than watching someone else do algebra. Enrollment is currently small (4 students), so I would like them to present derivations in class, under my watchful eye. (It might be the first time I ever grade students on "participation", which will be interesting too.)

What have y'all seen and/or done? General thoughts about teaching advanced heavy-on-the-derivations classes are welcome too.

I just finished teaching a similar course, I didn't use Griffiths as a text. Material for the fine and hyperfine structure of Hydrogen was taken from Cohen-Tannoudji. One advantage of smaller classes is the flexibility- you can alter the course content to suit the student's interests. For the final 1/3 of the semester, we covered field quantization (chapters taken from here and there), QED and electroweak theories (again, with material taken from here and there).

For homework and exams, I had the students work through journal articles- mostly derivations (for example, 'derive the result shown in equation 12').

Have fun with this course!

 

[Scott Hill]

Frankly, I'm intimidated by this course. I've never taught quantum mechanics before, haven't even thought about Schrödinger's equation much in the past decade, and it's all something of a blur. With a textbook I'll be fine, but I don't have a good enough feel for the subject to say "Oh yes, I really need to cover this topic or that topic next, once we're through Griffiths." It's going to be a lot of hard work.

 

[Herman Trivilino]

Frankly, I'm intimidated by this course. I've never taught quantum mechanics before, haven't even thought about Schrödinger's equation much in the past decade, and it's all something of a blur. With a textbook I'll be fine, but I don't have a good enough feel for the subject to say "Oh yes, I really need to cover this topic or that topic next, once we're through Griffiths." It's going to be a lot of hard work.

All the more reason to consider McIntyre. It's a more modern approach with emphasis on bra-ket notation and makes use of a nice piece of simulation software.

 

[Scott Hill]

All the more reason to consider McIntyre. It's a more modern approach with emphasis on bra-ket notation and makes use of a nice piece of simulation software.

It's probably too late to swap textbooks, but I'll get a copy for my own reference at least. Thanks!

 

[Herman Trivilino]

It's probably too late to swap textbooks, but I'll get a copy for my own reference at least. Thanks!

I doubt it's too late. Especially for such a small class.

 

[Andy Resnick]

Frankly, I'm intimidated by this course. I've never taught quantum mechanics before, haven't even thought about Schrödinger's equation much in the past decade, and it's all something of a blur. With a textbook I'll be fine, but I don't have a good enough feel for the subject to say "Oh yes, I really need to cover this topic or that topic next, once we're through Griffiths." It's going to be a lot of hard work.

Hang on- maybe I was confused. Here, 'advanced' QM means second semester, the first semester is 'intro' QM. What topics are you covering? What is are the expectations regarding student preparation- for example, have they had a class in differential equations yet? What is your background- what Physics (or engineering, or math) courses are you most comfortable teaching?

(One of) the complaint(s) I have with Griffiths' book is that each problem is solved differently, using specialized 'tricks', rather than a single unified approach.

As for swapping/changing textbooks, you can always 'supplement' the book with xeroxes/pdfs taken from other sources; this is easy since you only have a few students.

 

[Herman Trivilino]

(One of) the complaint(s) I have with Griffiths' book is that each problem is solved differently, using specialized 'tricks', rather than a single unified approach.

I've never taught the course and haven't even finished reading McIntyre, but the reason I bought was for the unified approach, starting with Stern-Gerlach. I read a review. I think it was in Physics Today about two years ago. I tried searching their online data base but ran out of time.

 

[Scott Hill]

Hang on- maybe I was confused. Here, 'advanced' QM means second semester, the first semester is 'intro' QM. What topics are you covering? What is are the expectations regarding student preparation- for example, have they had a class in differential equations yet? What is your background- what Physics (or engineering, or math) courses are you most comfortable teaching?

This is the last quantum mechanics class they will take before they graduate, if that helps. Differential equations and linear algebra are prerequisites. The catalog description is "Formalism and applications of quantum mechanics: Hilbert space, time-independent and time-dependent perturbation theories, atomic and molecular structure and spectra, and scattering theory," which is basically a summary of Griffiths' book.

I'm a long-term adjunct and my relationship with this department is complicated—not all bad, mind you. When asked if I could teach this class, I said "sure!" because that's how I get paid and because it's good to stretch myself. I've taught sophomore/junior-level thermal physics for a while now, and I taught an advanced E&M class out of Griffiths' other book a few years ago; otherwise it's been introductory level classes.

 

[Andy Resnick]

I've never taught the course and haven't even finished reading McIntyre, but the reason I bought was for the unified approach, starting with Stern-Gerlach. I read a review. I think it was in Physics Today about two years ago. I tried searching their online data base but ran out of time.

Haven't read McIntyre, but I almost used Townsend which seems to be very similar. I ended up using Kroemer's book, which I like very much.

The reason I didn't use Townsend is that (IMO) for a first exposure to the material, students need to think about the wavefunction as a real, concrete, function- they've already had some experience solving similar problems in E&M, and so making the jump to (say) a particle in a box means the students can more easily see the commonalities in math and not get distracted by 'interpretation' concepts. Also, it's easier to establish concepts like 'operators', 'orthonormal states', 'expectation values', etc. when actual functions are available to work with. Then, once they understand (to the extent that anyone can understand) the wavefunction as representing the state of a particle, I introduce bra-ket notation and can get a little more abstract.

To the OP- if you can, get a copy of Galitski's "Exploring Quantum Mechanics"- it's a large book of solved problems that may help alleviate some of your anxiety.

 

[Andy Resnick]

This is the last quantum mechanics class they will take before they graduate, if that helps. Differential equations and linear algebra are prerequisites. The catalog description is "Formalism and applications of quantum mechanics: Hilbert space, time-independent and time-dependent perturbation theories, atomic and molecular structure and spectra, and scattering theory," which is basically a summary of Griffiths' book.

Hmmm... that sounds like a quantum II class, not a quantum I class: quantum I should have things like "1-D particle in a box, 1-D harmonic oscillator, Hydrogen atom..." Do you have any course materials from the previous instructor to guide you? If you PM me, I can email you what I have.

I'm a long-term adjunct and my relationship with this department is complicated—not all bad, mind you. When asked if I could teach this class, I said "sure!" because that's how I get paid and because it's good to stretch myself. I've taught sophomore/junior-level thermal physics for a while now, and I taught an advanced E&M class out of Griffiths' other book a few years ago; otherwise it's been introductory level classes.

Ok, now I better understand your trepidation. I suspect if you spent a little time re-acquainting yourself with the basics you'll feel more confident. As I mentioned above, Galitski's book consists of worked examples. And I'm sure you know that there's an infinite amount of useful class notes out on the interweb. Start by creating a course outline- aside from the catalog list, what topics do you want to cover? Teaching QM II is an opportunity to really dig into all kinds of interesting topics, so pick those that you are interested in learning more about!

 

[Scott Hill]

Yes, I will be spending my Christmas vacation boning up on Quantum I, so that I'm at least at the same starting point they are. :)

 

[Herman Trivilino]

Hmmm... that sounds like a quantum II class, not a quantum I class: quantum I should have things like "1-D particle in a box, 1-D harmonic oscillator, Hydrogen atom..." Do you have any course materials from the previous instructor to guide you? If you PM me, I can email you what I have.

He did say they have a full year of modern physics before this class. Likely there's a lot of quantum physics in there, which is why they call this course "advanced."

I'd definitely get familiar with what was taught, and how, in that modern class.