Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The math of QM

  1. Apr 3, 2005 #1
    What kind of math does QM use (beyond calculus, differential equations and linear algebra)?
     
  2. jcsd
  3. Apr 3, 2005 #2
    Some complex analysis helped me quite a bit.
     
  4. Apr 3, 2005 #3
    So basically all the topics of multivariate calculus, complex analysis (including special functions), calculus of variations (a generalization of calculus), fourier analysis and functional analysis. I guess that modern topics in algebra such as groups, rings and fields are also very helpful.
     
  5. Apr 4, 2005 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Less on rings and fields,but a lotta group theory representations...

    Daniel.
     
  6. Apr 4, 2005 #5

    selfAdjoint

    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    Unless you get beyond basic QM, when rings (in the form of algebras: rings with a product) and fields get very important. Lie algebras, Von Neumann algebras, Clifford algebras, ...
     
  7. Apr 4, 2005 #6
    If one goes behind non-relativistic QM, there are the huge fields of modern analysis, abstract algebra, and topology. There are no clear boundaries.
     
  8. Apr 4, 2005 #7

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Of course not.This is theoretical physics,after all.There's never too much mathematics...

    Daniel.

    P.S.Did someone mention diff.geom.for nice bundle homological & cohomological approaches to quantization (including the famous BRST)...?
     
  9. Apr 4, 2005 #8

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    One might add Probability Theory, Logic, and Symplectic Geometry.
     
  10. Apr 4, 2005 #9
    I think that symplectic manifolds and nambu dynamics can be seen as a branch of symplectic topology and even differential topology. Thus, one might also add global analysis to this.
     
  11. Apr 11, 2005 #10
    Don't forget vector-cross-product math. Angular momentum and its orthogonality aspect extend not only from QM atomic orbits to also the perpenicularity of the axis of magnetic rotation of the Milky Way relative to the plane of matter. Cheers, Jim
     
    Last edited: Apr 11, 2005
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: The math of QM
  1. QM and maths? (Replies: 2)

Loading...