Integrable and superintegrable systems with spin in three-dimensional Euclidean space

A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spins 0 and is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components of linear momentum. Several such systems are found and for one nontrivial example we show how superintegrability leads to exact solvability: we obtain exact (nonperturbative) bound-state energy formulas and exact expressions for the wave functions in terms of products of Laguerre and Jacobi polynomials.