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Prove that the nth energy level of atom has degeneracy n^2

  1. Oct 27, 2015 #1
    1. The problem statement, all variables and given/known data
    Prove that the nth energy level of an atom has degeneracy equal to n^2.

    2. Relevant equations


    3. The attempt at a solution
    I was thinking of using the sum from n=1 to N of n = N(N+1)/2 but my professor said i needed to change that equation up a bit to be able to show this. I was also thinking about how l is less than or equal to n-1 and ml is less than l so both of those are sort of n's and together they are n squared? Overall a bit confused.
     
  2. jcsd
  3. Oct 27, 2015 #2

    mfb

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    2016 Award

    Staff: Mentor

    Something along that line I guess.
    I guess you can use the rules for allowed l and m and don't have to derive them?
     
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