# On a Fractional Schr\"odinger equation in the presence of Harmonic potential

## TL;DR

This paper investigates the existence and stability of solutions to a fractional Schr"odinger equation with harmonic potential, providing numerical insights into the dynamics and effects of different terms.

## Contribution

It establishes ground state existence and orbital stability for a fractional Schr"odinger equation with harmonic potential, including numerical analysis of the dynamics.

## Key findings

- Existence of ground state solutions
- Orbital stability of standing waves
- Numerical comparison of dynamics

## Abstract

In this paper, we establish the existence of ground state solutions for a fractional Schr\"odinger equation in the presence of a harmonic trapping potential. We also address the orbital stability of standing waves. Additionally, we provide interesting numerical results about the dynamics and compare them with other types of Schr\"odinger equations. Our results explain the effect of each term of the Schr\"odinger equation : The fractional power, the power of the nonlinearity and the harmonic potential.