Integrable and superintegrable systems with spin

Abstract

A system of two particles with spin s=0 and s=1/2 respectively, moving in a plane is considered. It is shown that such a system with a nontrivial spin-orbit interaction can allow an 8 dimensional Lie algebra of first-order integrals of motion. The Pauli equation is solved in this superintegrable case and reduced to a system of ordinary differential equations when only one first-order integral exists.

12 pages

References in corpus (5)

• Superintegrability with third order invariants in quantum and classical mechanics
• Exact Solvability of Superintegrable Systems
• Hamiltonians separable in cartesian coordinates and third-order integrals of motion
• Integrable and superintegrable quantum systems in a magnetic field
• Integrable Hamiltonian systems with vector potentials

Cited by in corpus (25)

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• Construction of classical superintegrable systems with higher order integrals of motion from ladder operators
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• Superintegrable systems with spin and second-order integrals of motion
• Matrix superpotentials and superintegrable systems for arbitrary spin
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• Integrability and supersymmetry of Schroedinger-Pauli equations for neutral particles
• Laplace-Runge-Lenz vector for arbitrary spin
• Integrable and superintegrable systems with spin in three-dimensional Euclidean space
• Superintegrable systems with spin invariant with respect to the rotation group
• Laplace-Runge-Lenz vector with spin in any dimension
• Superintegrable systems with spin and second-order (pseudo)tensor integrals of motion
• Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras
• Family of nonstandard integrable and superintegrable classical Hamiltonian systems in non-vanishing magnetic fields
• Recurrence approach and higher rank polynomial algebras for superintegrable monopole systems
• Doubly Exotic $N$th-order Order Superintegrable Classical Systems Separating in Cartesian Coordinates
• Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 2. Systems with dilatation and shift symmetries
• Dynamical symmetry in a minimal dimeric complex
• Second-order integrals for systems in $E_2$ involving spin
• Superintegrability in the interaction of two particles with spin