Supersymmetric η operators

Abstract

Being chosen as a differential operator of a special form, the metric η operator has become unitary equivalent to a one-dimensional Hermitian Hamiltonian with a natural supersymmetric structure. We show that fixing the superpartner of this Hamiltonian permits us to determine both the metric operator and the corresponding non-Hermitian Hamiltonian. Moreover, under an additional restriction on the non-Hermitian Hamiltonian, it has become a superpartner of another Hermitian Hamiltonian.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.