$\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians

TL;DR

This paper introduces a new class of spherically symmetric non-Hermitian Hamiltonians and their ta-weak-pseudo-Hermiticity generators, providing an operator-based method applicable to various radial quantum models.

Contribution

It presents a novel operator-based approach for constructing ta-weak-pseudo-Hermiticity generators for spherically symmetric Hamiltonians, extending previous 1D results to radial systems.

Findings

Derived ta-weak-pseudo-Hermiticity generators for specific non-Hermitian radial models

Extended the framework to include nodeless and non-nodeless states

Applied the method to radial oscillators, Coulomb, and Morse potentials

Abstract

A class of spherically symmetric non-Hermitian Hamiltonians and their \eta-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 \eta-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.