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How can get the eigenvalues of the two spin entangle

  1. Nov 20, 2008 #1
    there is a equation for two spins in entangled
    Hamiltonian: H=J([tex]\vec{\sigma}^1\cdot\vec{\sigma}^2+\vec{\sigma}^2\cdot\vec{\sigma}^1[/tex])+B([tex]\vec{\sigma}^1_z+\vec{\sigma}^2_z[/tex])

    where [tex]\vec{\sigma}^i=(\sigma^i_x,\sigma^i_y,\sigma^i_z)[/tex] are the pauli matrics for the ith (i=1,2) spin. J is the exchange constant ,

    My difficulties: how can we solve the Hamiltonian to get the four eigenvalues?

    thank you for helping me, and i want a detail reprentation.
  2. jcsd
  3. Nov 20, 2008 #2


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    Simply let H act on your four different spin states.

    The triplet S_tot = 1, M=+1,0,-1

    and the singlet S_tot = 0, M =0

    Good luck
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