The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator (Q2928118)

Mathematics, particularly algebra, has undoubtedly great merit and ability in making clear to a questioning mind the deep secrets of science of the material world. The paper under review is an excellent example of this fact through investigating the notion of quantum harmonic oscillator, one of the major corner stones of quantum physics, the chief basis of modern scientific research using quantum algebra.NEWLINENEWLINE The purpose of the authors' work here consists in the determination of the algebra of the generalized Chebyshev-Koornwinder oscillator and study of its properties. The article has 8 main sections including the Introduction and Conclusion. Detailed preliminaries are provided in the second section while next the algebra of generalized sectorial oscillator is developed. The fourth section treats algebra of generalized radial oscillator with the fifth section that deals with the boundary oscillator case. Then the Chebyshev-Koornwinder-oscillator is investigated, the last but one section being devoted to some special algebras.NEWLINENEWLINE In this 23-page interesting paper there are 50 references, 3 appendices, 3 figures and 107 equations altogether.