4 papers
Para families of orthogonal polynomials
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Krawtchouk polynomials arose in the search for spin chains with perfect state transfer; the para-Racah, -para-Racah and para-Bannai--Ito polynomials followed, obtained…
The supersymmetric Scarf I Hamiltonian with reflections and its discrete para-Bannai--Ito version
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para-Bannai--Ito polynomials are orthogonal on a Bannai--Ito bi-lattice that is \emph{two-sided} --- it extends on both sides of a central value --- and depend, besides t…
The para--Racah Hamiltonian as an exactly solvable discretization of the Pöschl--Teller box
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para--Racah Hamiltonian is the Jacobi matrix of the para--Racah polynomials, taken at the persymmetric value of their isospectral deformation parameter: a mirror--symmetric…
The para--Krawtchouk oscillator and its continuum limit
Stéphane Z. Beaulac, Nicolas Crampé, Quentin Labriet +3
The para--Krawtchouk polynomials define, through their recurrence relation, a finite oscillator model that carries out fractional revival. We determine the continuum limit of this…