Complex Optical Potentials and Pseudo-Hermitian Hamiltonians

Abstract

Recently some authors have broadened the scope of canonical quantum mechanics by replacing the conventional Hermiticity condition on the Hamiltonian by a weaker requirement through the introduction of the notion of pseudo-Hermiticity. In the present study we investigate eigenvalues, transmission and reflection from complex optical potentials enjoying the property of pseudo-Hermiticity.

11 pages, 8 figures, submitted to Physics Letters A, typos added

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Cited by in corpus (30)

• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Scattering in PT-symmetric quantum mechanics
• Delta-Function Potential with a Complex Coupling
• Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics
• Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method
• Bound states of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method
• New features of scattering from a one-dimensional non-Hermitian (complex) potential
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• Application of Pseudo-Hermitian Quantum Mechanics to a PT-Symmetric Hamiltonian with a Continuum of Scattering States
• Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential
• Analytically Solvable PT-Invariant Periodic Potentials
• PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
• Spectral singularity and deep multiple minima in the reflectivity in non-Hermitian (complex) Ginocchio potential
• The band spectrum of periodic potentials with PT-symmetry
• Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
• Absorption in atomic wires
• PT-Invariant Periodic Potentials with a Finite Number of Band Gaps
• On the Dirac equation with PT-symmetric potentials in the presence of position-dependent mass
• Coherent perfect absorption with and without lasing in complex potentials
• Quantum dynamics and relaxation in comb turbulent diffusion
• Exact Solutions of the Schrödinger Equation with position-dependent effective mass via general point canonical transformation
• Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
• Tailoring one-dimensional layered metamaterials to achieve unidirectional transmission and reflection
• Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
• Coherent scattering from semi-infinite non-Hermitian potentials
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• Acoustic response in a a one-dimensional layered pseudo-Hermitian metamaterial containing defects
• Reciprocity in parity violating non-Hermitian systems