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Linear Algebra thats needed in QM?

  1. Feb 19, 2008 #1

    so im currently taking LA + Diff. eqtns in one class right now. Im planning to take QM in the summer.

    So im wondering, how much of LA is needed for QM? My reason for askign this is that there are so many theorems and properties of matricis that i honestly can't master all of them, and i have difficulty understanding the proofs of many theorems. I'm wondering how much QM uses LA?

    What are the topics that i need to have down solidly?
    Also, are DE important in QM?
  2. jcsd
  3. Feb 19, 2008 #2
    You'll going to use matrices and that eigenvalues/eigenvectors stuff quite a bit. IMO, I say I used more LA than DE in QM
  4. Feb 19, 2008 #3
    Well, I don't know what your LA class covers, but eigenvalues and eigenvectors are important. Hamiltonian operators are nice to know, same with Hermitian Operators.

    In reality, I think a lot of the LA you see will be knowing the language. I don't think anyone expects you to maser LA, but it's important to be comfortable speaking in those terms used in LA.
  5. Feb 19, 2008 #4
    LA and Diff EQ's are important for QM, but I wouldn't worry too much. I had over a year's break between LA and QM and I still remembered enough to feel comfortable in the class.

    Only the very basics will be used, things like taking a determinant, eigenvalues, eigenvectors, etc. The nice thing about QM is that all of your operators are Hermitian, so that limits what you will potentially use. Overall it's not that bad.

    As for Diff EQ's, I've only had to "use" it a few times, and it was only in derivations. I've never had to actually use it to solve a problem. Well, none of the really complicated stuff. What you usually do is separation of variables, which is pretty easy, and solve from there.
  6. Feb 20, 2008 #5
    They usually teach you all the LA you need in an advanced undergraduate QM class. All you need to get by is sophomore level LA. I've found that in QM, I learn a lot of LA without even being aware that I'm learning LA. I actually took an LA course after senior quantum. Every couple of days I'd find myself saying, "hey, I know about that!" So I don't think it's that important to worry about mastering LA before studying quantum. You need to know the basics, like matrix multiplication, linear operators, eigenstuff, etc. But that's about it.
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