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Matrix Hamiltonian?

  1. Jun 27, 2008 #1
    Matrix Hamiltonian???

    1. The problem statement, all variables and given/known data

    I have two non-identical spin 1/2 particles, which have vector magnetic moments S_1 and S_2. The interaction energy (Hamiltonian) is given by a constant times the dot product of S_1 and S_2. There is no external field present.

    I need to find the eigenstates and eigenenergies, which I could easily do if the Hamiltonian was given as a matrix. Is there a way to write this H as a matrix or is there perhaps another way to find the eigen-items?

    Thanks so much for any input!!
     
  2. jcsd
  3. Jun 27, 2008 #2
    Re: Matrix Hamiltonian???

    Since these spin-1/2 particles there are only two possible eigenstates for each of the particles: either S=(1,0)[tex]^{T}[/tex] or (0,1)[tex]^{T}[/tex]. Since these are non interacting particles, either one can be in either state, so you have 4 possible configurations for the system. Then it's just a matter of chugging through the algebra.


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    theUndergrad

    http://www.theUndergraduateJournal.com/
     
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