Superintegrability and higher order polynomial algebras II

Understand

In an earlier article, we presented a method to obtain integrals of motion and polynomial algebras for a class of two-dimensional superintegrable systems from creation and annihilation operators.

• We discuss the general case and present its polynomial algebra.
• We will show how this polynomial algebra can be directly realized as a deformed oscillator algebra.
• This particular algebraic structure allows to find the unitary representations and the corresponding energy spectrum.