Closed formula for the metric in the Hilbert space of a PT-symmetric model

Abstract

We introduce a very simple, exactly solvable PT-symmetric non-Hermitian model with real spectrum, and derive a closed formula for the metric operator which relates the problem to a Hermitian one.

LaTeX, 13 pages; to appear in Journal of Physics A

References in corpus (2)

• PT-symmetric quantum mechanics
• Point Interactions: PT-Hermiticity and Reality of the Spectrum

Cited by in corpus (27)

• Mathematical and physical aspects of complex symmetric operators
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• Discrete PT-symmetric models of scattering
• Non-Hermitian Hamiltonians of Lie algebraic type
• A return to observability near exceptional points in a schematic PT-symmetric model
• Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem
• PT-symmetric deformations of Calogero models
• Non-Hermitian spectral effects in a PT-symmetric waveguide
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Three solvable matrix models of a quantum catastrophe
• Exact Isospectral Pairs of PT-Symmetric Hamiltonians
• Quantum star-graph analogues of PT-symmetric square wells
• Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration
• Solvable non-Hermitian discrete square well with closed-form physical inner product
• Metric operators for non-Hermitian quadratic su(2) Hamiltonians
• Quantum graphs: self-adjoint, and yet exhibiting a nontrivial $\mathcal{P}\mathcal{T}$-symmetry
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
• Quantum star-graph analogues of PT-symmetric square wells. II: Spectra
• On S-matrix of Schrodinger Operators with Non-Symmetric Zero-Range Potentials
• PT-symmetric dynamical confinement: Fermi acceleration, quantum force and Berry phase
• Discrete spectrum of thin PT-symmetric waveguide
• CPT-symmetric discrete square well
• Origin of folded bands in metamaterial crystals
• Surprising spectra of PT-symmetric point interactions
• Bifurcation of nonlinear eigenvalues in problems with antilinear symmetry
• Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity