Need help for Formalisms in Quantum Physics

October 24, 2007 9:40 AM

I badly need help on formalisms in Quantum Mechanics! I just read this post from 2 years ago, and it did help a little, but not really enough.

Story in short: I'm an aerospace engineering second-year, the pioneer batch of a trial academic program at my university. Suffice to say that additional requirements were put on us, and due to some poor course planning on the part of the administrators (don't ask) I'm almost at the end of a semester which saw me taking Linear Algebra I, II and Quantum Mechanics I simultaneously, without any prior knowledge/training in either of them.

Needless to say I'm not doing too well; I'm not too concerned about my grade - I should do well enough to pass, but I'd like to go further than that by the time the exams roll around in... about 4 weeks.

I'm just past the Schrodinger equations and recently started on formalisms for personal revision (about 6 lectures behind the course), and while the initial part was manageable I'm now deep under in Hilbert Space and Hermitian operators (x & iD), Fourier transforms and the like. I know it's not actually this hard; much of it seems like it should be intuitive and easily understandable if framed in the right context.

I know I should seek out my lecturer, but he isn't a great communicator by any measure, and while I'm pretty sure he's competent in the subject I can never understand anything he says. I am currently reading Introduction to Quantum Mechanics by David Griffiths, which has been quite a big help but still a little inaccessible for someone who's only spent 10 weeks on linear algebra thus far.

Finally, my query: Does anyone know of resources (preferably online) that greatly aids in understanding formalisms in the context of quantum physics? I know from personal experience that there is no substitute for practice, but with 4 weeks left to go I fear my revision isn't proceeding quickly enough, and I believe that some enlightening perspectives will help speed up my pace of revision.

I hope not to have to buy another textbook at this point; I won't be taking Quantum II next semester. While this will likely not be my last encounter with quantum physics, my future needs in this area are probably application-based (engineering-oriented) and not so theoretical, and spending that kind of money isn't really justified IMO. I'd seek out a library or cheap ebooks, but not anything more than that.

I know I'm trying to seek an easy way out of this mess, but if anyone can post something that helps I will be immensely thankful.

posted by kureshii to science & nature (7 comments total)

You've probably found these, but in case you haven't:

Quantum Mechanics for Engineers
Supplementary Notes, Quantum Mechanics

These two sites were helpful when I was making my way through QM last year (mechanical engineering background, now in graduate school in materials science).
posted by Mapes at 10:03 AM on October 24, 2007

To expand: QM is difficult, and massively difficult when you're trying to learn it en masse under the gun. It helps to divide the content into smaller pieces and focus on only one piece a day.

For example, get a few QM books out of the library (different levels, from beginner to Dirac), and line up your online resources in a few bookmarks. Now tackle Hermitian operators: what are their characteristics? What are they used for? How are they used in your class? Do a few sample problems, and write everything down: the standard steps, the parts where you get lost, any questions that come to mind. Remember that any information that you won't be graded on is extraneous, for now. Now you have your own resource, a primer that you can use the next day when you're familiarizing yourself with the uncertainty principle or wavefunctions. Keep doing topic by topic, scanning online and through books to capture the common message.

Also, if you're puzzled in a certain area, independently ask a few bright classmates to distill the concept into key points. In my experience, this is a win-win situation; if they give great answers, use them to your advantage. If they can't, then your smartest colleagues probably aren't far ahead of you after all, so what are you worrying about?
posted by Mapes at 10:19 AM on October 24, 2007

One more thing: I know you're looking chiefly for online resources, but this book is so, so good: Understanding Quantum Physics, a User's Manual. Easily readable, understandable, totally useful. If you can get it at your library, I think it's just what you're looking for.
posted by Mapes at 10:26 AM on October 24, 2007

It sounds like you could use a tutor. Too bad your lecturer is no good. Check out Physics Forums. Post specific questions. Look into other threads with Q&As.

Also, I'd talk to the lecturer and explain your situation (no pre-requisites, not going to take QMII etc) and they might give you a few extra problems to work on. I took QM in the undergrad (now I am in diff physics field) and all I remember is that solving *a lot* of problems was very important in understanding things. Good luck.
posted by carmina at 10:29 AM on October 24, 2007

I'm now deep under in Hilbert Space and Hermitian operators (x & iD), Fourier transforms and the like. I know it's not actually this hard; much of it seems like it should be intuitive and easily understandable if framed in the right context.

These things are actually not intuitive. If you're just taking linear algebra right now, I'm guessing that you haven't taken any functional analysis, which is the mathematical framework underlying hilbert spaces and hermitian operators and the like. This is fairly deep mathematics that requires comfort with linear algebra, abstract algebra, and real analysis.

I don't have a concrete resource for you, and (not to be pessimistic, but...) I think that if you're taking linear algebra for the first time right now, there is little chance that you're going to be able to understand Hilbert spaces and that sort of stuff within the next four weeks.

My suggestion is to make sure that you know what all the symbols stand for, even if you don't know all the theory behind them. And make sure you can do the problems. Ask other students, read the sample problems in Griffiths, see if there are solutions posted somewhere, etc. Do the problems over and over again, writing them out each time, so you at least get a feel for how they work and the kind of techniques you're supposed to use.
posted by number9dream at 10:39 AM on October 24, 2007

Make sure you're taking Griffiths slowly enough. It's a small book, but it takes a lot of work to get through. Getting through just the first four chapters in a semester is an accomplishment. I'm sure you've already looked at chapter three, but look at it again. Also a good portion of the material is in the homework questions; by all means do them.

And I wouldn't be too worried about not having the linear algebra experience. Griffiths explains most of the linear algebra whenever it comes up. Plus there's the appendix, which is a good overview.

Personally I would never put too much importance on the formalism. In one semester of QM, 90% of the goal is to acquaint you with the idea of wavefunctions, measurement, and some solutions to the Schrödinger equation. The intricacies of Hilbert space might be interesting, but they're not something you need to understand in one semester.
posted by kiltedtaco at 7:13 PM on October 24, 2007

Thanks for the responses! Understanding Quantum Physics, a User's Manual will be available in the library on 5 Nov, I'll try to get my hands on it then. Meanwhile, I'm picking up various other library books on the subject as well. I'm not hoping for an A; not that it matters, but since I'm already taking the module for better or worse I'd like to understand as much as I can before my attention gets diverted to other modules next semester.

I'll try to keep all this advice in mind.
posted by kureshii at 5:33 AM on October 26, 2007