A generalized non-Hermitian oscillator Hamiltonian, N-fold supersymmetry and position-dependent mass models

Abstract

A generalized non-Hermitian oscillator Hamiltonian is proposed that consists of additional linear terms which break PT-symmetry explicitly. The model is put into an equivalent Hermitian form by means of a similarity transformation and the criterion of N-fold supersymmetry with a position-dependent mass is shown to reside in it.

9 pages, no figures; minor corrections, to appear in Physics Letters A

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• Remarks on the Solution of the Position Dependent Mass (PDM) Schrödinger Equation
• New 1-step extension of the Swanson oscillator and superintegrability of its two-dimensional generalization
• The Quantum Effective Mass Hamilton-Jacobi Problem
• $\mathcal{P}\mathcal{T}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
• Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
• Non-Hermitian Oscillator and R-deformed Heisenberg Algebra
• Exploring Branched Hamiltonians for a Class of Nonlinear Systems
• Dirac equation in curved spacetime: the role of local Fermi velocity
• CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework
• A generalized Swanson Hamiltonian in a second-derivative pseudo-supersymmetric framework
• Exact solution for the time dependent non-Hermitian generalized Swanson oscillator
• Non-hermitian Dirac Hamiltonian in the presence of local Fermi velocity
• Revisited Swanson's Hamiltonian