η-Weak-Pseudo-Hermiticity Generators and Radially Symmetric Hamiltonians

Abstract

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

Torsion effects on a relativistic position-dependent mass system

“…[23] as a position-dependent mass system. It is worth mentioning other interests in position-dependent mass systems, such as, in PT -symmetric quantum mechanics [25][26][27], supersymmetric quantum mechanics [28][29][30] and relativistic quantum mechanics [31][32][33][34][35][36][37].…”

Non-Hermitian d-dimensional Hamiltonians with position-dependent mass and their η-pseudo-Hermiticity generators

“…In this work, we present (in section 2) a d-dimensional recipe for η-pseudoHermiticity generators for a class of non-Hermitian Hamiltonians with positiondependent masses, M (r) = m • m (r) . An immediate recovery of our generalized η-pseudo-Hermiticity generators for Hamiltonians with radial symmetry [14] is obvious through the substitution m (r) = 1. Our illustrative examples are given in section 3.…”

“…In a broader class (where PT -symmetric Hamiltonians constitute a subclass among others) of non-Hermitian pseudo-Hermitian Hamiltonians [8][9][10][11][12][13][14] (a generalization of PT -symmetry, therefore), it is concreted that the eigenvalues of a pseudo-Hermitian Hamiltonian H are either real or come in complex-conjugate pairs. In this case, a Hamiltonian H is pseudo-Hermitian if it obeys the similarity transformation:…”

“…for some linear invertible operator O : H→H (where H is the Hilbert space of the quantum system with a Hamiltonian H) and satisfies the intertwining relation (cf., e.g., [12,14] and references therein)…”

“…In a recent study [14], we have presented a class of spherically symmetric nonHermitian Hamiltonians and their η-pseudo-Hermiticity generators. Therein, a generalization beyond the nodeless 1D states is proposed and illustrative examples are presented, including an exactly solvable non-Hermitian η-pseudoHermitian Morse model.…”