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What level of math do I need to study Quantum Mechanics?

  1. Jun 24, 2010 #1
    I've been comparing program requirements for a specialist in Physics and a specialist in Mathematical Physics. Obviously the latter requires more math courses, but the exact same amount of physics courses. Furthermore, in the physics program they don't require too much math which I find strange as I thought physics would require a lot of higher level math courses - especially for Quantum Mechanics.

    What level of math do I need to study Quantum Mechanics? Could you be specific? Like Real Analysis, Complex Analysis, Topology, Differential Geometry, Lie Theory etc...
  2. jcsd
  3. Jun 24, 2010 #2
    You will need to take differential equations and applied math after that which gets you to think completely in 3-D, I took a course in tensors which really helps when you exploit the orthonormality of a function using the kronecker delta, makes quantum incredibly easier.
  4. Jun 24, 2010 #3
    So I will have to have studied the math I mentioned above? All of it?
  5. Jun 24, 2010 #4
    As long as you have good common sense you can figure out most anything in physics, plus its physics-math, everything has real meaning to it.
  6. Jun 24, 2010 #5
    But could you maybe tell me specifically what courses you'd recommend a student to take? Because I would think that you'd more than common sense as if I don't have the necessary math background I wouldn't understand equations and such...
  7. Jun 24, 2010 #6
    You could always look in the academic calendar of whatever institution you're considering applying to, and find the prerequisites for the quantum mechanics course(s) offered.
  8. Jun 24, 2010 #7
    Seconded. Prerequisites are usually a good indicator. Be comfortable with calculus and familiar with the concept of partial derivatives. Knowing a little linear algebra, particularly the concept of a vector space, helped me as well in my beginning quantum mechanics class. If your course is like mine, what will happen is that the professor will go over most of the math you need along with the physics. For example, in my course, we needed some Fourier analysis; it was taught to us.
  9. Jun 24, 2010 #8
    At the undergraduate level, you'll need partial differential equations. Linear algebra and complex analysis would be useful, but it's something you can pick up during the course.

    You aren't going to need topology, differential geometry, or Lie theory at the undergraduate level.
  10. Jun 25, 2010 #9


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    As always, at undergraduate level physics you won't need any advanced mathematics, and the standard linear algebra, differential equations, complex analysis (or: calculus) will suffice. But the most important mathematics used in QM is Functional Analysis. If you're going to study the more technical aspects of QM, everything will involve functional analysis.
  11. Jun 25, 2010 #10
    I found that with a second year Linear Algebra course I got by just fine in QM even up to the graduate course level.
  12. Jun 25, 2010 #11
    Ahh I see, thanks a lot to everyone!! :D
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