English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We revisit the MIC-harmonic oscillator in flat space with monopoleinteraction and derive the polynomial algebra satisfied by the integrals ofmotion and its energy spectrum using the ad hoc recurrence approach. Weintroduce a superintegrable monopole system in generalized Taub-NUT space. TheSchr\"{o}dinger equation of this model is solved in spherical coordinates inthe framework of St\"{a}ckel transformation. It is shown that wave functions ofthe quantum system can be expressed in terms of the product of Laguerre andJacobi polynomials. We construct ladder and shift operators based on thecorresponding wave functions and obtain the recurrence formulas. By applyingthese recurrence relations, we construct higher order algebraically independentintegrals of motion. We show the integrals form a polynomial algebra. Weconstruct the structure functions of the polynomial algebra and obtain thedegenerate energy spectra of the model.

Recurrence approach and higher rank polynomial algebras for superintegrable monopole systems