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

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Winternitz P., Yurdusen İ.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.42, no.38, 2009 (SCI-Expanded) identifier identifier


A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particleswith spins 0 and 1/2 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.