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Electron Angular Momentum

  1. Nov 18, 2009 #1
    1. Here's the problem:
    Consider a system of two electrons, each with l = 1 and s = 1/2.
    (A) What are the possible values of the quantum number for the total orbital angular momentum L = L1 + L2?
    (B) What are the possible values of the quantum number for the spin orbital angular momentum S = S1 + S2?
    (C) Using the above results, find the possible values of the quantum number for the total orbital angular momentum J = L + S.
    (D) What are the possible individual quantum numbers j1 and j2 for the total angular momentum of each electron separately?
    (E) Use the results of part (D) to compute the allowed values of j from the possible combinations of j1 and j2. Do your results agree with those of part (C)?

    2. Relevant equations
    L = [STRIKE]h[/STRIKE][l(l + 1)]1/2
    S = [STRIKE]h[/STRIKE][s(s + 1)]1/2
    J = [STRIKE]h[/STRIKE][j(j + 1)]1/2


    3. The attempt at a solution
    (A) since l = 1,
    L1 = [STRIKE]h[/STRIKE][l(l + 1)]1/2 = [STRIKE]h[/STRIKE](2)1/2
    I think this can be positive or negative, so
    L = 2[STRIKE]h[/STRIKE](2)1/2, or -2[STRIKE]h[/STRIKE](2)1/2, or 0.

    (B) I did this the same as (A) except with 1/2 instead of 1. I got:
    S = [STRIKE]h[/STRIKE](3)1/2, or -[STRIKE]h[/STRIKE](3)1/2, or 0

    (C) I assume just add up all the possibilities for L and S

    (D) j = l + s or j = l - s
    so, j = 1/2 or j = 3/2

    (E) total j = 1 or 2 of 3
    so J = [j (j + 1)]1/2
    so, J = [STRIKE]h[/STRIKE](21/2)
    or [STRIKE]h[/STRIKE](61/2)
    or 2[STRIKE]h[/STRIKE](31/2)

    Basically I'm really unsure about (A) and (B). I have more confidence in (D) and (E), and (C) should be easy once I get the first two.
     
  2. jcsd
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