Superintegrable systems with spin in two- and three-dimensional Euclidean spaces

The concept of superintegrability in quantum mechanics is extended to the case of a particle with spin s=1/2 interacting with one of spin s=0. Non-trivial superintegrable systems with 8- and 9-dimensional Lie algebras of first-order integrals of motion are constructed in two- and three-dimensional spaces, respectively.Comment: 7 page

Superintegrable Systems with a Third Order Integrals of Motion

Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of motion are not the same in classical and quantum mechanics is stressed. New results on the use of classical and quantum third order integrals are presented in Section 5 and 6.Comment: To appear in J. Phys A: Mathematical and Theoretical (SPE QTS5