Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. I. First steps
Exactly Solvable and Integrable Systems
2014-10-06 v1 Mathematical Physics
Classical Analysis and ODEs
math.MP
Quantum Algebra
Abstract
We present and develop a recursion scheme to construct joint eigenfunctions for the commuting analytic difference operators associated with the integrable N-particle systems of hyperbolic relativistic Calogero-Moser type. The scheme is based on kernel identities we obtained in previous work. In this first paper of a series we present the formal features of the scheme, show explicitly its arbitrary-N viability for the `free' cases, and supply the analytic tools to prove the joint eigenfunction properties in suitable holomorphy domains.
Keywords
Cite
@article{arxiv.1206.3787,
title = {Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. I. First steps},
author = {Martin Hallnäs and Simon Ruijsenaars},
journal= {arXiv preprint arXiv:1206.3787},
year = {2014}
}
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44 pages