Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    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

    kith

    User Avatar
    Science Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Eigenvectors, spinors, states, values
Loading...