Quantum Sturm-Liouville Equation, Quantum Resolvent, Quantum Integrals, and Quantum KdV : the Fast Decrease Case

TL;DR

This paper develops quantum operators for the quantum Sturm-Liouville and resolvent equations, demonstrating conserved currents and relying on quantum fields and regularization techniques.

Contribution

It introduces a novel construction of quantum operators for classical equations, establishing conservation laws in the quantum setting.

Findings

Existence of quantum operators solving quantum Sturm-Liouville and resolvent equations

Proof of conserved currents in the quantum framework

Dependence on quantum field data and regularization methods

Abstract

We construct quantum operators solving the quantum versions of the Sturm-Liouville equation and the resolvent equation, and show the existence of conserved currents. The construction depends on the following input data: the basic quantum field $O(k)$ and the regularization .