# Quantum Well in Fractional Quantum Mechanics

## TL;DR

This paper derives an exact energy spectrum solution for a particle in a quantum well within fractional quantum mechanics, introduces a graphical method for energy level determination, and discusses implications for emulating fractional quantum effects.

## Contribution

It provides the first exact solution for energy levels in a fractional quantum well and a simple graphical algorithm for their calculation.

## Key findings

- Exact energy spectrum derived for fractional quantum well
- Graphical algorithm for energy level determination
- Potential for emulating fractional quantum mechanics in quantum wells

## Abstract

Within the framework of fractional quantum mechanics, an exact solution has been found for the energy spectrum of a quantum particle confined in a quantum well - a symmetric one-dimensional finite potential well. A simple graphical algorithm is described for obtaining the number of discrete levels in a quantum well and their associated energy values. The presented results open up new possibilities for emulating fractional quantum mechanics using quantum wells.