Operator Domains and SUSY Breaking in a Model of SUSYQM with a Singular Potential

Abstract

The self-adjoint extension of the symmetric supercharges and Hamiltonian of a model of Supersymmetric Quantum Mechanics on the half-line, for the case of a singular superpotential, is analyzed. The compatibility of the domains of definition of the different operators and the possibility of effectively implement the graded superalgebra in a dense subspace of the Hilbert space is considered. As a consequence, conditions for SUSY breaking in this model are established.