Supersymmetric Quantum Mechanics: Light at the End of the (Quantum) Tunnel

TL;DR

This paper develops the foundations of quantum mechanics through supersymmetry, focusing on superpotentials, shape invariant potentials, and their matrix/operator representations, linking to the eigenstate thermalization hypothesis.

Contribution

It introduces a supersymmetric framework for quantum mechanics, emphasizing shape invariance and matrix modeling, advancing theoretical understanding of quantum systems.

Findings

Superpotential methods derive supersymmetric partner potentials.

Shape invariant potentials facilitate solvable models.

Matrix and operator models connect to thermalization hypotheses.

Abstract

In this project, we will develop the foundations of quantum mechanics using the methods of supersymmetry. We will discuss the use of the superpotential to derive the supersymmetric partner of a potential in one dimension, and explore several key examples with an emphasis on shape invariant potentials. We will then discuss the modeling of supersymmetric quantum systems using matrices and operators, and how it relates to the eigenstate thermalization hypothesis.