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Spin,orbital and total angular momentum

  1. Mar 14, 2013 #1

    ShayanJ

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    Gold Member

    In the section "Angular momentum in quantum mechanics" of the angular momentum page in wikipedia,one can find the following:
    But we know that spin is an intrinsic property of a particle,a property that can be used for its identification.So how is it that it is not conserved?
    I mean,we say that e.g. electrons' spin is 1/2.If spin is not conserved,then what is this 1/2?

    Thanks
     
  2. jcsd
  3. Mar 14, 2013 #2

    jtbell

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    Staff: Mentor

    The magnitude of the spin angular momentum is fixed:

    $$S = \sqrt{s(s+1)} \hbar = \sqrt{\frac{1}{2} \left( \frac{1}{2}+1 \right)} \hbar
    = \frac{\sqrt{3}}{2} \hbar$$

    but the component along any direction (usually we call it the z-direction) can change:

    $$S_z = m_s \hbar = \pm \frac{1}{2} \hbar$$

    that is, it can be either "spin up" or "spin down".
     
  4. Mar 15, 2013 #3

    Meir Achuz

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    In J=L+S, the S can be the total spin of several electrons. The 1/2 spin of each electron can add up to different spin S values.
     
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