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Dual -1 Hahn polynomials and perfect state transfer
Luc Vinet, Alexei Zhedanov
We find all the spin chains with perfect state transfer (PST) that are connected with the dual -1 Hahn polynomials . For odd we recover a model that had alr…
Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain with perfect state transfer
Luc Vinet, Alexei Zhedanov
Analogs of Krawtchouk polynomials defined on a bi-lattice are introduced. They are shown to provide a (novel) spin chain with perfect transfer. Their characterization is given as w…
d-Orthogonal polynomials and su(2)
Vincent X. Genest, Luc Vinet, Alexei Zhedanov
Two families of d-orthogonal polynomials related to su(2) are identified and studied. The algebraic setting allows their full characterization (explicit expressions, recurrence rel…
An infinite family of superintegrable Hamiltonians with reflection in the plane
Sarah Post, Luc Vinet, Alexei Zhedanov
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schrödinger equations admit separ…
Dynamical Invariants and Berry's Phase for Generalized Driven Harmonic Oscillators
Barbara Sanborn, Sergei K. Suslov, Luc Vinet
We present quadratic dynamical invariant and evaluate Berry's phase for the time-dependent Schroedinger equation with the most general variable quadratic Hamiltonian.
Supersymmetric Quantum Mechanics with Reflections
S. Post, L. Vinet, A. Zhedanov
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Sc…