Supersymmetric Quantum Mechanics: The Duality of Two Elementary Models

Abstract

This undergraduate thesis contains one dimensional introductory treatment of Supersymmetric Quantum Mechanics (SUSY QM). The factorisation method is used to obtain Partner Hamiltonians, and the notions of partner potentials and superpotential are introduced. It demonstrated how energy spectra and eigenfunctions of partner potentials can be correlated for the cases of unbroken and broken supersymmetry. Generalisations of these cases attributed to Sets of Hamiltonians and shape invariant potentials are introduced. The devel oped formalisation is used to obtain energy eigenfunctions and spectra of partner potentials of some well-known quantum systems, namely the Infinite Square Well and the Free Particle. In these systems, the partner potentials are trigonometric and hyperbolic functions, respectively. A comparison of these two physically distinct but mathematically related partner potentials is provided. A new philosophical interpretation of SUSY QM is introduced, with an ontological discussion of supersymmetric notions and SUSY QM. The current observation problem of SUSY is discussed, and on that basis, two opposing arguments are presented. The method of Falsification by Karl Popper is briefly introduced, and an argument is produced regarding its application to SUSY.