On supersymmetries in nonrelativistic quantum mechanics

TL;DR

This paper investigates supersymmetries in one-dimensional nonrelativistic quantum systems with time-independent potentials, classifying their invariance Lie superalgebras and analyzing the structure of even and odd supersymmetries.

Contribution

It provides a systematic classification of supersymmetries and their invariance superalgebras in nonrelativistic quantum mechanics, expanding understanding of symmetry structures.

Findings

Classification of supersymmetries in nonrelativistic systems

Identification of invariance Lie superalgebras

Tables summarizing supersymmetry structures

Abstract

One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed out. The study of even supersymmetries is particularly enlightened through the already known symmetries of the corresponding Schr\"odinger equation. Three tables collect the even, odd, and total supersymmetries as well as the invariance (super)algebras.