Superintegrable systems with spin and second-order integrals of motion

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 $V_0=\frac{\alpha }{r}+\frac{3{\hslash }^2}{8r^2}$ and spin orbital one $V_1=\frac{\hslash }{2r^2}$.

32 pages

References in corpus (7)

• Superintegrable Systems in Darboux spaces
• Hamiltonians separable in cartesian coordinates and third-order integrals of motion
• Integrable and superintegrable systems with spin
• Polynomial Poisson Algebras for Classical Superintegrable Systems with a Third Order Integral of Motion
• An infinite family of superintegrable systems from higher order ladder operators and supersymmetry
• Non-relativistic scattering of a spin-1/2 particle off a self-dual monopole
• Infinite families of superintegrable systems separable in subgroup coordinates

Cited by in corpus (14)

• Classical and Quantum Superintegrability with Applications
• New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials
• Fourth order Superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials
• Superintegrable systems with position dependent mass
• Laplace-Runge-Lenz vector for arbitrary spin
• Recurrence approach and higher rank cubic algebras for the $N$-dimensional superintegrable systems
• Symmetries of the Schroedinger-Pauli equations for charged particles and quasirelativistic Schroedinger equations
• Superintegrable systems with spin and second-order (pseudo)tensor integrals of motion
• Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
• Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups
• 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
• Second-order integrals for systems in $E_2$ involving spin
• Runge-Lenz Vector as a 3d Projection of SO(4) Moment Map in ${\mathbb{R}}^4\times {\mathbb{R}}^4$ Phase Space
• Superintegrability in the interaction of two particles with spin