Quadratic algebra for superintegrable monopole system in a Taub-NUT space

Abstract

We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the corresponding Schrodinger equation of the Hamiltonian is separable in both spherical and parabolic coordinates. We obtain the integrals of motion of this superintegrable model and construct the quadratic algebra and Casimir operator. This algebra can be realized in terms of a deformed oscillator algebra and has finite dimensional unitary representations (unirreps) which provide energy spectra of the system. This result coincides with the physical spectra obtained from the separation of variables.

18 pages

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Cited by in corpus (8)

• Fourth order Superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials
• Family of nonstandard integrable and superintegrable classical Hamiltonian systems in non-vanishing magnetic fields
• Algebraic approach and exact solutions of superintegrable systems in 2D Darboux spaces
• On superintegrable monopole systems
• Recurrence approach and higher rank polynomial algebras for superintegrable monopole systems
• Infinite dimensional representations of cubic and quintic algebras and special functions
• Superintegrable families of magnetic monopoles with non-radial potential in curved background
• Generalized MICZ-Kepler systems on three-dimensional sphere and hyperboloid