1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integrating Laguerre Polynomials - Fine structure hydrogen

  1. Jan 28, 2006 #1
    Hi

    I have the following problem:
    To calculate the fine structure energy corrections for the hydrogen atom, one has to calculate the expectation value for (R,R/r^m), where R is the solution of the radial part of the schroedinger equation (i.e. essentially associated laguerre polynomial) and m=1,2,3.
    [tex]\int_{0}^{\infty} {dx} {(\mathrm{L}_n^k)}^2e^{-x}x^{k+1-m}[/tex]
    Solving the integral for n=1 is easy because the laguerre polynomials are normalised that way.
    For m=2,3 it is much harder. I have already spent a few hours trying to get a solution by using the generating function of the laguerre polynomials, but no luck yet. Can anybody give me a hint how to do it?

    Thx
    Sebastian

    Edit:
    Can anybody tell me how to post latex in this forum pls. Sorry for my stupidity, but I just don't get it.
    Edit 2: Thx for the help on latex Statuts X. Added integral to the post.
     
    Last edited: Jan 29, 2006
  2. jcsd
  3. Jan 28, 2006 #2

    StatusX

    User Avatar
    Homework Helper

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Integrating Laguerre Polynomials Date
Fourier transform of integral e^-a|x| Today at 8:15 AM
Cylindrical Coordinates Triple Integral -- stuck in one place Yesterday at 9:00 PM
Time derivative of gravity due to acceleration Apr 11, 2018
Integration Question Help Apr 10, 2018
Rodrigues’ formula of Laguerre Oct 16, 2015