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Quantum State

  1. Oct 17, 2008 #1
    1. The problem statement, all variables and given/known data
    n = 3
    Using the fact that there are two quantum states for each value of l and m because of electron spin. Find the total number of electron states with n = 3.


    2. Relevant equations



    3. The attempt at a solution
    I've already determined that l = 0, 1, 2
    and m = -2, -1, 0, 1, 2

    So, given the information I figured it would be 8 * 2 = 16 quantum states.
    Unfortunately, it's supposed to be 18 quantum states and I fail to see where they pick up 2 extra ones. Does anyone know what I am doing incorrectly?
     
  2. jcsd
  3. Oct 17, 2008 #2
    Well for n = 3...

    Set l = 2:
    then m can take on the range of: -2,-1,0,1,2

    Set l = 1:
    m = {-1,0,1}

    l = 0:
    m = 0

    There's 9 states.

    EDIT: Think of, for n = 3, every independent quantum state by labelling your state:

    [tex]\psi_{n,l,m}: \psi_{3,0,0} \neq \psi_{3,1,-1} \neq \psi_{3,1,0}[/tex]

    and so on..
     
    Last edited: Oct 17, 2008
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