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Eigenstate of a spin operator

  1. Mar 6, 2016 #1
    1. The problem statement, all variables and given/known data
    I have a spin operator and have to find the eigenstates from it and then calculate the eigenvalues.
    I think I managed to get the eigenvalues but am not sure how to get the eigenstates.


    2. Relevant equations
    gif.gif

    3. The attempt at a solution
    I think I managed to get the eigenvalues out to be ±1 by forming the following matrix
    gif.gif
     
  2. jcsd
  3. Mar 6, 2016 #2

    vela

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    That matrix is wrong. What is ##\lambda##? What does ##\sin^{\pm i\lambda}## even mean?

    Have you really never found eigenvectors for a matrix? It's typically covered in lower-division linear algebra and differential equations. It seems a bit strange that you'd be in a course asking you to do this problem without having taken the math courses.
     
  4. Mar 6, 2016 #3
    Apologies the ##\sin^{\pm i\lambda}## is incorrect and meant to say ##\sin^{\pm i\varphi}## and yes I have taken eigenvectors before, just not one similar to this.
     
  5. Mar 7, 2016 #4

    blue_leaf77

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    That doesn't make sense either.
     
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