In quantum mechanics, the Pauli equation, or Schrödinger–Pauli equation, is the formulation of the Schrödinger equation for spin-½ particles, which takes into account the interaction of the particle's spin with an external electromagnetic field. It is the non-relativistic limit of the Dirac equation and can be used where particles are moving at speeds much less than the speed of light, so that relativistic effects can be neglected. It was formulated by Wolfgang Pauli in 1927.
$$ \left[\frac{1}{2m}(\sigma\cdot(\hat{p}-qA))^{2}+q\phi\right]|\psi\rangle=i\hbar\frac{\partial}{\partial t}|\psi\rangle $$________________________________________
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Author of the notes: Antonio J. Pan-Collantes
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