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Eigenvectors, spinors, states, values

  1. Mar 8, 2012 #1
    For spin-1/2, the eigenvalues of [itex]S_x, S_y[/itex] and [itex]S_z[/itex] are always [itex]\pm \frac{\hbar}{2}[/itex] for spin-up and spin-down, correct?

    What is the difference between eigenvectors, eigenstates and eigenspinors? I believe eigenstates = eigenspinors and eigenvectors are something else? I'm just getting confused, because my teachers use the letter [itex]\chi[/itex] for everything.
  2. jcsd
  3. Mar 9, 2012 #2


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    Hi SoggyBottoms! :wink:

    I think "eigenvector" is the correct technical term for integral spin, and "eigenspinor" for half-integral spin.

    But i wouldn't worry about it. :smile:
  4. Mar 9, 2012 #3
    So all three terms are actually the same? At least as far as my introductory QM is concerned? Eigenvector = eigenspinor = eigenstate?
  5. Mar 9, 2012 #4


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    well, not exactly the same, since a spinor isn't a vector, and a vector isn't a spinor

    but your introductory QM probably doesn't go into the difference between vectors and spinors in detail anyway o:)
  6. Mar 9, 2012 #5
    It doesn't indeed, but they use all the terms interchangeably it seems, so it's confusing. Thanks.
  7. Mar 9, 2012 #6


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    State is short for state vector, so eigenstate and eigenvector are the same. These terms are general and apply to every quantum system.

    Spinors are a specific way to express spin state vectors. For spin 1/2 particles, they have two or four components (Pauli spinor vs. Dirac spinor).

    State vectors are written as |ψ>. If you want to write them in a specific base, you use column vector notation (<a1|ψ> <a2|ψ> ... )T. The same notation is often used for spinors, although rectangular brackets are arguably better to make it clear you are talking about spinors: χ=[c1 c2]T.
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