Structure of Matrix Elements in Quantum Toda Chain

TL;DR

This paper analyzes the matrix elements in the quantum Toda chain using separation of variables, expressing them through deformed Abelian integrals and discussing their properties in relation to classical theory.

Contribution

It introduces a novel representation of matrix elements in the quantum Toda chain via deformed Abelian integrals and explores their properties.

Findings

Matrix elements are expressed as finite deformed Abelian integrals.

Properties of these integrals are essential for the independence of operators.

Comparison with classical theory clarifies the quantum-classical correspondence.

Abstract

We consider the quantum Toda chain using the method of separation of variables. We show that the matrix elements of operators in the model are written in terms of finite number of ``deformed Abelian integrals''. The properties of these integrals are discussed. We explain that these properties are necessary in order to provide the correct number of independent operators. The comparison with the classical theory is done.