Solutions for the L\'evy-Leblond or parabolic Dirac equation and its generalizations

TL;DR

This paper derives solutions for the Levy-Leblond and parabolic Dirac equations using hypergeometric functions and spherical harmonics, and extends the method to a broader class of Dirac operators with four parameters.

Contribution

It introduces a novel approach to solving specific Dirac equations and generalizes the method to a wider family of operators with multiple parameters.

Findings

Solutions expressed in hypergeometric functions and spherical harmonics.

Generalization to Dirac operators depending on four parameters.

Applicable to a broader class of Dirac-type equations.

Abstract

In this paper we determine solutions for the L\'evy-Leblond operator or a parabolic Dirac operator in terms of hypergeometric functions and spherical harmonics. We subsequently generalise our approach to a wider class of Dirac operators depending on 4 parameters.