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Pavel Winternitz
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Superintegrable systems with spin
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We present a classification of superintegrable
systems involving the interaction of a particle
0f spin 1/2 with one of spin zero. The systems
are assumed to be spherically symmetric and
are hence integrable ( since energy and total
angular momentum are conserved). We request
that they allow at least one further integral
of motion and hence they are superintegrable.
Among the systems presented is one
with a Coulomb scalar potential and a specific
spin-orbital interaction. It allows a vector
Laplace -Runge-Lenz integral of motion that
is a third order polynomial in the momenta.
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