The Schrödinger-Pauli equation is the non-relativistic limit of the Dirac equation, and therefore describes spin-1/2 particles in an external electromagnetic field. It is given by:
$$\left[\frac{1}{2m}(\boldsymbol{\sigma} \cdot (\boldsymbol{p}-q\boldsymbol{A}))^2+q\phi\right]|\psi\rangle=i \hbar\frac{\partial}{\partial t}|\psi\rangle.$$
Are there any analytical solutions to this equation? I have searched online but have unfortunately been unable to find any.