Multivariable Bessel polynomials related to a Calogero-Sutherland model

by Dr Martin Hallnäs (Chalmers University of Technology)

Tuesday 2 Dec 2008, 10:15 → 11:00 Europe/Stockholm

The (one-variable) Bessel polynomials, a classical family of orthogonal polynomials, first appeared in a paper by Bochner in 1929. Among their applications is the fact that they give the eigenfunctions of the bound states of a quantum particle in a so-called Morse potential. As is well-known, there is a an integrable multivariable generalisation of this model, where the interactions are given by the hyperbolic Calogero-Sutherland model. In this talk I will discuss a multivariable generalisation of the Bessel polynomials which similarly give the eigenfunctions of bound states in this multiparticle model. In particular, I will show that they are orthogonal with respect to the relevant Hilbert space inner product, and compute their norms. Thus providing a set of normalised, and mutually orthogonal, eigenfunctions of the hyperbolic Calogero-Sutherland model with external Morse potential.