Abstract
In elementary particle physics, supersymmetry (SUSY) (Wess and Zumino, 1974) is a symmetry which relates half-integral spin particles (fermions) to particles with integral spin (bosons). Using the supersymmetric version of SU(5) or SO(10), it was possible to unify electromagnetic, weak, and strong interactions. There is no experimental evidence for the existence of new SUSY particles in nature. On the other hand, applications of SUSY have been found in nuclear and condensed matter physics as well. Applications of supersymmetry in nonrelativistic quantum mechanics was first discussed by Witten (1981). The aim of this paper is to analyze the inverse square potentials using supersymmetric quantum mechanics. First we discuss how to construct supersymmetric algebra in quantum mechanics. Introducing SUSY quantum mechanics, then we analyze inverse square potentials in that context. Supersymmetric quantum mechanics has a close relationship to supersymmetric field theory. Supersymmetric one-particle quantum mechanics serves as a model for the investigation of spontaneous breaking of supersymmetry, which is supposed to occur in supersymmetric field theories. Now consider a one-particle quantum mechanical system in one dimension.
Published Version
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