Supersymmetric Quantum Mechanics: two factorization schemes, and quasi-exactly solvable potentials

Abstract

We present the general ideas on SuperSymmetric Quantum Mechanics (SUSY-QM) using different representations for the operators in question, which are defined by the corresponding bosonic Hamiltonian as part of SUSY Hamiltonian and its supercharges, which are defined as matrix or differential operators. We show that, although most of the SUSY partners of one-dimensional Schr\"odinger problems have already been found,there are still some unveiled aspects of the factorization procedure which may lead to richer insights of the problem involved.