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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.
I cannot be sure, but I suspect that you can get analytical solutions of the Pauli equation by taking a non-relativistic limit of analytical solutions of the Dirac equation. The latter can be found in many books, say Bagrov, Vladislav G. / Gitman, Dmitry, The Dirac Equation and its Solutions (http://www.degruyter.com/view/product/177851) (you can find a Google preview). One example of an analytical solution of the Pauli equation can be found in http://arxiv.org/abs/physics/9807019 .
