Author

Nicolas Cramp'e

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Preprint Sep 2026

The supersymmetric Scarf I Hamiltonian with reflections and its discrete para-Bannai--Ito version

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 $c_0$ --- and depend, besides the two grid parameters, on an isospectral deformation parameter. Their Jacobi matrix $J$ is invariant under the reversal of the sites at one...

Stéphane Z. Beaulac, Nicolas Cramp'e, Q. Labriet et al. · 2 citations

Preprint Sep 2026

The para--Krawtchouk oscillator and its continuum limit

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 Hamiltonian, both from its recurrence relation and directly on the polynomials. The limit is the singular (isotonic) oscillator $-\partial_\...

Stéphane Z. Beaulac, Nicolas Cramp'e, Q. Labriet et al. · 2 citations