Factorization of the Schr\"{o}dinger Operator and the Riccati Equation in the Clifford Analysis Setting

TL;DR

This paper explores the factorization of the higher-dimensional Schrödinger operator within Clifford analysis, providing new insights into its mathematical structure and potential applications in quantum mechanics and mathematical physics.

Contribution

It introduces a novel factorization approach for the Schrödinger operator using Clifford analysis, extending classical methods to higher dimensions.

Findings

New factorization formulas for the Schrödinger operator

Extension of classical factorization techniques to higher dimensions

Potential applications in quantum physics and mathematical analysis

Abstract

This paper is devoted to a factorization of the higher dimensional Schrodinger operator in the framework of Clifford analysis.