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Integrable and superintegrable systems with spin

P. Winternitz·I. Yurdusen
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Abstract

A system of two particles with spin s=0 and s=1/2 respectively, moving in a plane is considered. It is shown that such a system with a nontrivial spin-orbit interaction can allow an 8 dimensional Lie algebra of first-order integrals of motion. The Pauli equation is solved in this superintegrable case and reduced to a system of ordinary differential equations when only one first-order integral exists.

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P. Winternitz, I. Yurdusen. 2007-11-05. Integrable and superintegrable systems with spin. https://doi.org/10.1063/1.2360042

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