Quadratic symmetry algebras and Sturm algebraization of superintegrable systems with magnetic fields
The study analyzes two three-dimensional quantum superintegrable systems with magnetic fields using three algebraic methods to describe their energy spectra. It shows that the system's integrals generate a quadratic algebra, which relates to deformed oscillators. Furthermore, after separation of variables, the equations can be described by sl(2) and sl(3) algebras derived from Sturm eigenvalue problems, revealing common hidden structures despite the systems being distinct.