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Moments in QM

  1. Jul 12, 2009 #1
    [tex]\vec{J}[/tex] - mechanical moment
    [tex]\vec{L}[/tex] - orbital moment
    [tex]\vec{S}[/tex] - spin moment

    [tex]\vec{J}=\vec{L}+\vec{S}[/tex]

    When can I say
    [tex]J^2\approx J(J+1)[/tex]
    [tex]L^2\approx L(L+1)[/tex]
    [tex]S^2\approx S(S+1)[/tex]?
     
  2. jcsd
  3. Jul 14, 2009 #2
    For large enough J, L and S :)
     
  4. Jul 14, 2009 #3

    clem

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    In your equations the J on the left is an operator, the j on the right should be an eigenvalue (a number). Then your equations always hold for angular momentum states of pure j,l,s.
     
  5. Jul 17, 2009 #4
    [tex]J[/tex] - eigen-value

    I'm asking you because the formula

    [tex]g_J=\frac{J(J+1)+L(L+1)-S(S+1)}{2J(J+1)}[/tex]

    I think that that formula is in the game not just for very large [tex]J,L,S[/tex].
     
  6. Jul 17, 2009 #5

    Fredrik

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    You always have [tex]\vec J\thinspace ^2|jm\rangle=j(j+1)|jm\rangle[/tex], but if the left-hand sides of your equations are eigenvalues too, then the equations are obviously only valid when J,L,S are negligible compared to J²,L²,S².
     
  7. Jul 17, 2009 #6

    clem

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    That formula is true for all eigenstates of J,L,S.
     
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