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I Why is the total number of quantum states = 2n^2 for some n?

  1. Mar 31, 2017 #1
    If the number of possible values of L is n, and the number of possible values of m is 2*L-1, and there are 2 spin directions.. shouldn't the total number of states be 2*(number of possible L)*(Number of possible m)? But this gives 4n^2 - 2n. I am extremely confused. Thanks for your help!
  2. jcsd
  3. Mar 31, 2017 #2


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    Staff: Mentor

    Each (different) value of l has a different number of possible of values of m, so you can't simply multiply (number of possible l)*(number of possible m).
  4. Mar 31, 2017 #3
    Looks to me like the values of l range from 0 to n-1 so no l value equals n.
    The number of possible values of l is n, but the values of l don't equal n.
  5. Mar 31, 2017 #4
    Oh, duh..thanks, definitely clears that up! Thank you!
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