Superintegrable systems with spin and second-order integrals of motion

2012/08/31 by Jean-Francois Desilets, Pavel Winternitz, Ismet Yurdusen
Mathematics · Physics and Astronomy · #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8113/45/47/475201

published as J. Phys. A: Math. Theor. 45 (2012) 475201 · 32 pages

arxiv created 2014/07/16 · arxiv updated 2015/06/11

Abstract

We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems which allow additional integrals of motion that are second order matrix polynomials in the momenta. These integrals are assumed to be scalars, pseudoscalars, vectors or axial vectors. Among the superintegrable systems obtained, we mention a generalization of the Coulomb potential with scalar potential V₀=\fracαr+(3ℏ²)/(8r²) and spin orbital one V₁=(ℏ)/(2r²).

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