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

Question about Orthogonal Polynomials

  1. May 7, 2012 #1
    Hello, I'm studing the hydrogen atom and I found an unified presentation of orhtogonal polynomials in the book by Fuller and Byron. I would like to learn more about it but in the same spirit(for physicits not for mathematicians). Can someone give some references where to find more?
     
  2. jcsd
  3. May 7, 2012 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Hmm, for physics usually a book like Byron-Fuller / Arfken / Morse & Feshbach would do. However, when you see the subject from the mathematical perspective, you can go deeper, into Hilbert space theory or into the analysis of hypergeometric functions which are the most natural generalizations.
     
  4. May 7, 2012 #3
    What do you mean, like Hermite polynomials? Bessel functions are also basically polynomials. And of course Legendre polynomials. I'd learn those, we use all those in QM.
     
  5. May 8, 2012 #4
    Arfken and Fuller presents clearly like a problem of eingenvalues of a selfadoint operator(sturn Liouville system) then he analyzes the conditions for the equation to render polynomials solution and from this one obteins all polynomials solutions(Hermite,Legendre,Laguerre,etc.) in a single framework and not like separate cases, for instance one can obtein a general Rodrigues formula encompassing all cases. It is very interesting and all done without fancy mathematics. I would very much like to see more of this, I mean more details, expleined by another author to complement the excellent presentation of Fuller/Byron
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question about Orthogonal Polynomials
Loading...