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

Abstract

A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 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 non-trivial 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.

23 pages

References in corpus (3)

• An infinite family of solvable and integrable quantum systems on a plane
• Hamiltonians separable in cartesian coordinates and third-order integrals of motion
• Integrable and superintegrable systems with spin

Cited by in corpus (9)

• Generalized MICZ-Kepler system, duality, polynomial and deformed oscillator algebras
• Superintegrable systems with position dependent mass
• Integrability and supersymmetry of Schroedinger-Pauli equations for neutral particles
• Laplace-Runge-Lenz vector for arbitrary spin
• Superintegrable systems with spin and second-order (pseudo)tensor integrals of motion
• Symmetries of the Schroedinger-Pauli equations for charged particles and quasirelativistic Schroedinger equations
• Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups
• Second-order integrals for systems in $E_2$ involving spin
• Superintegrability in the interaction of two particles with spin