Eigenfunctions of $GL(N,\RR)$ Toda chain: The Mellin-Barnes representation

TL;DR

This paper derives recurrence relations for eigenfunctions of $GL(N, r)$ Toda chains and constructs a Mellin-Barnes integral representation for their explicit form, advancing understanding of quantum integrable systems.

Contribution

It introduces a new recursive method linking eigenfunctions of $GL(N, r)$ and $GL(N-1, r)$ Toda chains and provides an explicit Mellin-Barnes integral representation for the $N$-particle case.

Findings

Derived recurrence relations between eigenfunctions of $GL(N, r)$ and $GL(N-1, r)$ Toda chains.

Constructed Mellin-Barnes integral representation for $N$-particle eigenfunctions.

Enhanced analytical tools for quantum Toda chain eigenfunction analysis.

Abstract

The recurrent relations between the eigenfunctions for $GL(N,\RR)$ and $GL(N-1,\RR)$ quantum Toda chains is derived. As a corollary, the Mellin-Barnes integral representation for the eigenfunctions of a quantum open Toda chain is constructed for the $N$-particle case.