# Spin-orbit coupling

by Tianyou
Tags: coupling, spinorbit
 P: 4 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.