15 papers
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…
Classical Heun observables and elliptic solvability
Luc Vinet, Alexei Zhedanov
We introduce a classical analog of the algebraic Heun operator associated with a classical Leonard pair. Given two observables and satisfying the classical counterpart of t…
Rational Heun operators on -linear grids
Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
Rational Heun operators on the linear grid are presented. They are second-order difference operators constructively defined from the requirement that they have a rais…
Spectral surgery and high-fidelity quantum state transfer in chains
Luc Vinet, Alexei Zhedanov
We consider an inhomogeneous spin chain which interpolates between the Krawtchouk one with perfect state transfer and the homogeneous chain. This model can be used to per…
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…
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…