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Associated Laguerre polynomials .

  1. Dec 3, 2014 #1
    1. The problem statement, all variables and given/known data
    Show that L11(x) and L12(x) are precisely the polynomials for 1s and 2s orbitals. What is the role of variable x in each case?

    2. Relevant equations
    L1n(x) = d/dx Ln(x), n = 1, 2, 3...

    3. The attempt at a solution
    Because L1(x) = 1 - x
    L2(x) = 2 - 4x + x2:
    I did:
    L11(x) = d/dx L1(x) = d/dx (1 - x) = -1
    L12(x) = d/dx L2(x) = d/dx (2-4x+x2) = 2x - 4 = 2(x - 2)....I wonder if x is a different function of radius in 1s and 2s orbital polynomials? I am also confused as how to find polynomials for 1s and 2s orbitals? Could anyone hint pls?
    For sure, I undersand that
    L11(x)= 1 because of 0 nodes...hence 1s
    L12(x) = 2x -4 because of 1 node.....hence 2s
     
  2. jcsd
  3. Dec 9, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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