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

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Cited by in corpus (10)

• Embedding of the Racah Algebra R($\mathbf{n}$) and Superintegrability
• The classical Taub-Nut System: factorization, spectrum generating algebra and solution to the equations of motion
• Racah Algebra $R(n)$ from Coalgebraic Structures and Chains of $R(3)$ Substructures
• Two-dimensional superintegrable systems from operator algebras in one dimension
• The Perlick system type I: from the algebra of symmetries to the geometry of the trajectories
• Coalgebra symmetry for discrete systems
• Superintegrable systems, polynomial algebra structures and exact derivations of spectra
• General Nth order integrals of the motion
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Discrete-time systems in quasi-standard form and the ${\mathfrak{h}}_6$ coalgebra symmetry