Abstract
A class η-weak-pseudo-Hermiticity generators for spherically symmetric non-Hermitian Hamiltonians 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, and the non-Hermitian perturbed radial Coulomb.
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