# Laplace equation for the Dirac, Euler and the harmonic oscillator

## TL;DR

This paper provides explicit solutions to Laplace equations linked to the Dirac operator, Euler operator, and harmonic oscillator in real space, enhancing understanding of these fundamental differential operators.

## Contribution

It introduces explicit solutions for Laplace equations related to key operators in mathematical physics, which were previously not explicitly known.

## Key findings

- Explicit solutions for Laplace equations with Dirac, Euler, and harmonic oscillator operators.
- Improved understanding of the structure of these differential equations.
- Potential applications in mathematical physics and operator theory.

## Abstract

In this article, we give the explicit solutions to the Laplace equations associated to the Dirac operator, Euler operator and the harmonic oscillator in R.