Quantum Integrals from Coalgebra Structure

Abstract

Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. 2N-1 integrals, of arbitrary order, are constructed via a multi-dimensional version of the factorization method, thus confirming the conjecture of D Riglioni 2013 J. Phys. A: Math. Theor. 46 265207. The systems are extended via coalgebra extension of sl(2) representations, although not all integrals are expressible in these generators. As an example, dimensional reduction is applied to 4D systems to obtain extension and new proofs of the superintegrability of known families of Hamiltonians.

21 pages , 2 plots

References in corpus (4)

• Reduction of superintegrable systems: the anisotropic harmonic oscillator
• Hamiltonian systems admitting a Runge-Lenz vector and an optimal extension of Bertrand's theorem to curved manifolds
• Action-angle variables for dihedral systems on the circle
• N-dimensional sl(2)-coalgebra spaces with non-constant curvature

Cited by in corpus (3)

• The classical Taub-Nut System: factorization, spectrum generating algebra and solution to the equations of motion
• The Perlick system type I: from the algebra of symmetries to the geometry of the trajectories
• General Nth order integrals of the motion