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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…
Morse momentum wavefunctions and rational functions
Luc Vinet, Alexei Zhedanov
We revisit the bound states of the Morse potential in the momentum representation. After the ground-state factor is extracted, the remaining factors are finite rational functions o…
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…
Algebraic Leonard trio approach to rational functions: the Hahn case
Nicolas Crampé, Quentin Labriet, Lucia Morey +1
The finite families of Hahn polynomials and associated biorthogonal rational functions are interpreted algebraically in the framework of Leonard trios. We introduce the trio Hahn a…
The dynamical algebra of the generic superintegrable model on the two-sphere
Nicolas Crampé, Quentin Labriet, Lucia Morey +3
The rank two Jacobi algebra is identified as the dynamical algebra of the generic quadratic superintegrable model on the two-sphere. The physical representation of…
Ruijsenaars-van Diejen-Takemura Hamiltonians as rational Heun operators
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
The most general Ruijsenaars-van Diejen-Takemura Hamiltonians are characterized as Heun operators defined as second order -difference operators with a raising action on elementa…