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I see a Hamiltonian of spin-orbit coupling, it is like this

H=[itex]\frac{1}{2m} \sum_{\alpha} \left( \left( -\partial_{\alpha}^2 - 2i\kappa_{\alpha} \sigma_{\alpha} \partial_{\alpha} \right) + \kappa_{\alpha}^2\right)[/itex]

Here [itex]\hbar = 1. \kappa_{\alpha} [/itex] is the strength of spin-orbit coupling, and [itex] \sigma_{\alpha} (\alpha = x, y, z)[/itex] are Pauli matrices.

Can someone explain to me where this hamiltonian comes from? What is the meaning of each term?

Thank you.

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# Spin-orbit coupling

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