$η$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians

Abstract

A class of spherically symmetric non-Hermitian Hamiltonians and their η-weak-pseudo-Hermiticity generators are presented. An operators-based procedure is introduced so that the results for the 1D Schrodinger Hamiltonian may very well be reproduced. A generalization beyond the nodeless states is proposed. Our illustrative examples include η-weak-pseudo-Hermiticity generators for the non-Hermitian weakly perturbed 1D and radial oscillators, the non-Hermitian perturbed radial Coulomb, and the non-Hermitian radial Morse models.

14 pages, content revised/regularized to cover 1D and 3D cases