suppose that I want to take a graduate level QM course, what kind of math do I need?

would a solid knowledge on linear algebra and differential equations suffice?

If you've taken the undergraduate versions of these courses, you should have a pretty good idea. Math wise it will be pretty similar... except that the instructor probably won't be as lenient towards not understanding how to do a certain math operation. I've found that the difference between graduate and undergraduate is the amount of detail in derivations and problems. In undergrad, an instructor might use a hand waving argument to explain something about the hydrogen atom... in graduate school you'll work it out in full detail. Just an example.

For EM, knowing your vector calculus is probably top priority. Being confident with your integration tricks and various theorems like Greens, Stokes, etc. would probably be a good start.

Read a text like Calculus on manifolds by Spivak, this will prepare you for the calculus you need in E&M grad units.

marcusl
Gold Member
an undergrad course on math methods (especially special functions, orthogonal polynomials and complex variables) is also useful.

thanks for the advices. I will look into those topics. It looks like EM requires a more sophisticated mathematical background. I guess I'll stick to learning QM for now.

For EM, knowing your vector calculus is probably top priority. Being confident with your integration tricks and various theorems like Greens, Stokes, etc. would probably be a good start.

Here's a question from someone who'll be taking graduate E&M in the Fall. Are there ever any instances in which you've got to actually take a surface integral or a curl? Because in my undergrad course, I found that I never had to parametrize a surface, or do anything crazy like that (which is too bad, because I was actually good at that stuff back in multivariable calc). Should I be expecting problems like this in E&M? Or should I be expecting more of the specialized techniques like images, multipole expansions, etc.?

Yes and yes. I've found that EM really is a large exercise in any, and sometimes all, of your vector calculus abilities. I can't give specific examples since I don't have a book in front of me (and I also wasn't all that great at it anyway). If you're comfortable with it already it probably won't be a problem. If you have doubts, just do some refresher problems before the class starts. Its much easier to do that over the summer than to give yourself a crash course during the semester.

Tom Mattson
Staff Emeritus