# Definition Spin-orbit coupling (or spin-orbit interaction) is a relativistic effect that arises due the interaction between a particle's spin and its motion inside a potential. The [[Hamiltonian]] is: $ H = \lambda (\nabla V(\pmb{r}) \times \pmb{p}) \cdot \pmb{S} $ where $\lambda$ gives the strength of the interaction, $\pmb{p}$ is the electron momentum operator and $\pmb{S}$ is the [[Physics/Spin]] operator.