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Homework Help: Angular Momentum (Modern Physics)

  1. Oct 31, 2008 #1
    1. The problem statement, all variables and given/known data
    This problem is giving me a headache and unfortunately I can't find any example that is similar to it.
    A hydrogen atom is in the n = 3, l = 2 state.

    (a) What are the possible values of j?

    (b) What are the possible values of the magnitude of the total angular momentum including spin?

    (c) What are the possible z components of the total angular momentum?


    2. Relevant equations



    3. The attempt at a solution

    (a)
    I believe that jmax = l + 1/2
    and jmin = l - 1/2 so...
    jmax = 5/2
    jmin = 3/2
    so
    j = 5/2, 3/2

    (b)

    J = L + S
    J = sqrt( j (j+1) )

    J1 = sqrt(35)/2 hbar --> (j =5/2)
    J2 = sqrt(15)/2 hbar --> (j=3/2)


    (c)

    j = 3/2; mj = +- 3/2, +- 1/2
    j = 5/2; mj = +-5/2, +-3/2, +-1/2


    I am very unsure about this whole process. My book unfortunately doesn't have any examples of this process. Can anyone check my work and see if what I am doing is correct? In particular I am very unsure of part b, it just seems a bit strange to me despite following the formula.

    Thanks
    roeb
     
  2. jcsd
  3. Oct 31, 2008 #2
    it all looks correct!
     
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