Eigenfunctions of the van Diejen model generated by gauge and integral transformations

DOI10.1016/J.AIM.2022.108816arXiv2203.00498MaRDI QIDQ6392472

Farrokh Atai, M. Noumi

Publication date: 1 March 2022

Abstract: We present how explicit eigenfunctions of the principal Hamiltonian for the $B{C}_m$ relativistic Calogero-Moser-Sutherland model, due to van Diejen, can be constructed using gauge and integral transformations. In particular, we find that certain $BC$-type elliptic hypergeometric integrals, including elliptic Selberg integrals, of both Type I and Type II arise as eigenfunctions of the van Diejen model under some parameter restrictions. Among these are also joint eigenfunctions of so-called modular pairs of van Diejen operators. Furthermore, these transformations are related to reflections of the $E_8$ Weyl group acting on the space of model parameters.

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Exactly solvable models; Bethe ansatz (82B23) Integral transforms of special functions (44A20) Difference operators (39A70) Generalized hypergeometric series, ({}_pF_q) (33C20) Elliptic functions and integrals (33E05)

This page was built for publication: Eigenfunctions of the van Diejen model generated by gauge and integral transformations

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6392472)