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Eigenvalue of an hamiltonian with spin

  1. May 2, 2017 #1
    1. The problem statement, all variables and given/known data

    Finding eigenvalues of an hamiltonian

    2. Relevant equations


    H = a S²z + b Sz
    (hbar = 1)
    what are the eigenvalues of H in |S,M> = |1,1>,|1,0>,|1,-1>

    3. The attempt at a solution


    H|1,1> = (a + b) |1,1>
    H|1,0> = 0
    H |1,-1> = (a-b) |1,-1>

    which gives directly the energy :

    a+b , 0 , a-b

    is that right ? Actually I'm not sure about :

    S²z |S,M> = M² |S,M>


    After, I need to calculate the average value of the magnetic moment so I need to be sure of the energy
     
  2. jcsd
  3. May 2, 2017 #2

    kuruman

    User Avatar
    Homework Helper
    Gold Member

    That is correct. Think of it as two successive applications of Sz. You are good so far.
     
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