nicxm
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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.
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.