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math-ph2026
A discrete Smorodinsky--Winternitz II superintegrable system
Pierre-Antoine Bernard, Vutha Vichhea Chea, Luc Vinet
We construct a discrete Smorodinsky--Winternitz II superintegrable system on a triangular region of the two-dimensional square lattice. The model is built from a pair of commuting…
math-ph2026
A discrete Smorodinsky--Winternitz I superintegrable system
Vutha Vichhea Chea, Luc Vinet
We construct a finite discrete realization of the Smorodinsky--Winternitz I superintegrable system on a triangular region of the two-dimensional square lattice. The construction is…
math-ph2026
The 2D Smorodinsky--Winternitz II system and the Laguerre--Heun algebra
Vutha Vichea Chea, Luc Vinet, Alexei Zhedanov
We identify the quadratic symmetry algebra of the two-dimensional Smorodinsky--Winternitz II system with a Laguerre-type confluent Heun algebra. The system is separable in Cartesia…