Asymptotic estimates for the wave functions of the Dirac-Coulomb operator and applications

TL;DR

This paper derives uniform asymptotic estimates for confluent hypergeometric functions using steepest-descent, and applies these results to establish Strichartz estimates with angular derivative loss for the massless Dirac-Coulomb equation in three dimensions.

Contribution

It provides new uniform asymptotic estimates for special functions and applies them to analyze the Dirac-Coulomb operator, leading to improved Strichartz estimates.

Findings

Established uniform asymptotic estimates for confluent hypergeometric functions.

Derived Strichartz estimates with angular derivative loss for the Dirac-Coulomb equation.

Enhanced understanding of wave function behavior in quantum mechanics models.

Abstract

In this paper we prove some uniform asymptotic estimates for confluent hypergeometric functions making use of the steepest-descent method. As an application, we obtain Strichartz estimates with loss of angular derivatives for the massless Dirac-Coulomb equation in $3D$.