Symmetry and Integrability of Equations of Mathematical Physics − 2011

Anatoly Nikitin (Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)

Dual shape invariance and superintegrable models for arbitrary spin

Shape invariant matrix potentials are classified. It is demonstrated that some of such potentials can be generated by two non-equivalent superpotentials. We call this property dual shape invariance. Examples of physical models admitting dual shape invariance are discussed, and they are the superintegrable Pronko models for arbitrary spin. We prove that, in addition to the dynamical symmetry w.r.t. algebra O(1,2) these models are supersymmetric and dually shape invariant, and use these properties to construct their exact solutions.