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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.

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  • $\begingroup$ What do you mean by "analytical" solutions? It is a linear equation of evolution with a self-adjoint generator (under suitable assumptions); the solution is always written in terms of the related unitary group. Do you mean an explicit form of the unitary group? If that's the case, the answer is most likely no. $\endgroup$ – yuggib May 30 '16 at 4:34
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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 .

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