nicxm
Nov20-08, 11:49 PM
there is a equation for two spins in entangled
Hamiltonian: H=J(\vec{\sigma}^1\cdot\vec{\sigma}^2+\vec{\sigma} ^2\cdot\vec{\sigma}^1)+B(\vec{\sigma}^1_z+\vec{\si gma}^2_z)
where \vec{\sigma}^i=(\sigma^i_x,\sigma^i_y,\sigma^i_z) 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.
Hamiltonian: H=J(\vec{\sigma}^1\cdot\vec{\sigma}^2+\vec{\sigma} ^2\cdot\vec{\sigma}^1)+B(\vec{\sigma}^1_z+\vec{\si gma}^2_z)
where \vec{\sigma}^i=(\sigma^i_x,\sigma^i_y,\sigma^i_z) 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.