# Spin-orbit coupling

Hello,
I see a Hamiltonian of spin-orbit coupling, it is like this
H=$\frac{1}{2m} \sum_{\alpha} \left( \left( -\partial_{\alpha}^2 - 2i\kappa_{\alpha} \sigma_{\alpha} \partial_{\alpha} \right) + \kappa_{\alpha}^2\right)$

Here $\hbar = 1. \kappa_{\alpha}$ is the strength of spin-orbit coupling, and $\sigma_{\alpha} (\alpha = x, y, z)$ 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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DrDu
Where did you see it?

I saw this hamiltonian in an article in arXiv titled "Enhancement of condensate depletion due to spin-orbit coupling".

DrDu