Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators

Abstract

We present a generalized Kaluza-Klein monopole system. We solve this quantum superintegrable systems on a Euclidean Taub Nut manifold using the separation of variables of the corresponding Schroedinger equation in spherical and parabolic coordinates. We present the integrals of motion of this system, the quadratic algebra generated by these integrals, the realization in term of a deformed oscillator algebra using the Daskaloyannis construction and the energy spectrum. The structure constants and the Casimir operator are functions not only of the Hamiltonian but also of other two integrals commuting with all generators of the quadratic algebra and forming an Abelian subalgebra. We present an other algebraic derivation of the energy spectrum of this system using the factorization method and ladder operators.

13 pages

References in corpus (22)

• Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials
• Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability
• Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles
• An infinite family of superintegrable deformations of the Coulomb potential
• Superintegrability and higher order polynomial algebras I
• A Recurrence Relation Approach to Higher Order Quantum Superintegrability
• Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion
• Hidden symmetry of hyperbolic monopole motion
• Classification of quantum superintegrable systems with quadratic integrals on two dimensional manifolds
• Generalized MICZ-Kepler system, duality, polynomial and deformed oscillator algebras
• An infinite family of superintegrable systems from higher order ladder operators and supersymmetry
• Algebraic Calculation of the Energy Eigenvalues for the Nondegenerate Three-Dimensional Kepler-Coulomb Potential
• A new exactly solvable quantum model in N dimensions
• Curved manifolds with conserved Runge-Lenz vectors
• Non-commutative oscillator with Kepler-type dynamical symmetry
• 4D singular oscillator and generalized MIC-Kepler system
• Supersymmetric quantum mechanical generalized MIC-Kepler system
• The su(1,1) Dynamical Algebra for the Generalized MICZ-Kepler Problem from the Schrödinger Factorization
• An $su(1,1)$ algebraic approach for the relativistic Kepler-Coulomb problem
• Four-dimensional double singular oscillator
• The su(1,1) dynamical algebra from the Schrödinger ladder operators for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator
• Quadratic Algebra Approach to Relativistic Quantum Smorodinsky-Winternitz Systems

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• Quadratic algebra for superintegrable monopole system in a Taub-NUT space
• Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies
• Superintegrable systems, polynomial algebra structures and exact derivations of spectra
• On superintegrable monopole systems
• Recurrence approach and higher rank polynomial algebras for superintegrable monopole systems