Bethe Ansatz in Quantum Mechanics. 2. Construction of Multi-Parameter Spectral Equations

TL;DR

This paper introduces a straightforward method for constructing multi-parameter spectral equations in quantum mechanics, enabling the development of integrable and exactly solvable quantum systems using a novel scalar triangle functional relation.

Contribution

It presents a new approach utilizing the scalar triangle equation, akin to the Yang-Baxter equation, for building exactly solvable spectral equations in quantum systems.

Findings

Method successfully constructs multi-parameter spectral equations

Enables creation of integrable quantum models

Provides a new functional relation for spectral problem solving

Abstract

In this paper we propose a simple method for building exactly solvable multi-parameter spectral equations which in turn can be used for constructing completely integrable and exactly solvable quantum systems. The method is based on the use of a special functional relation which we call the scalar triangle equation because of its similarity to the classical Yang-Baxter equation.