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

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


    User Avatar
    Science Advisor
    Homework Helper

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

Have something to add?

Similar Discussions: How can get the eigenvalues of the two spin entangle