Must a Hamiltonian be Hermitian?
From MaRDI portal
Publication:3088666
DOI10.1119/1.1574043zbMath1219.81125arXivhep-th/0303005OpenAlexW3105448191WikidataQ62272474 ScholiaQ62272474MaRDI QIDQ3088666
Dorje C. Brody, Hugh F. Jones, Carl M. Bender
Publication date: 19 August 2011
Published in: American Journal of Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/hep-th/0303005
General and philosophical questions in quantum theory (81P05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)
Related Items
Time evolution for quantum systems with a dynamical Hilbert space, The missing piece of the jigsaw puzzle: probability conservation as a consequence of time-reversal symmetry, Complex periodic potentials with a finite number of band gaps, Approximate analytical description for the nonlinear ${ \mathcal P }{ \mathcal T }$-symmetric coupled-mode equations, Non-Hermitian Physics and Master Equations, The operational foundations of PT-symmetric and quasi-Hermitian quantum theory, A NOTE ON THE INTEGRABILITY OF NON-HERMITIAN EXTENSIONS OF CALOGERO–MOSER–SUTHERLAND MODELS, PT-symmetric quantum graphs, \(\mathcal{PT}\)-symmetric peakon solutions in self-focusing/defocusing power-law nonlinear media: stability, interactions and adiabatic excitations, Minimal and maximal lengths from position-dependent non-commutativity, An accurate European option pricing model under fractional stable process based on Feynman path integral, Locally Definitizable Operators: The Local Structure of the Spectrum, Solution to the ghost problem in fourth order derivative theories, Harmonic oscillators from displacement operators and thermodynamics, On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation, Similarity transformations of Hermitian Hamiltonians and pseudo-Hermitian coupling between two electromagnetic modes, Isospectrality of spherical MHD dynamo operators: Pseudo-hermiticity and a no-go theorem, Krein-space formulation of \(\mathcal{PT}\) symmetry, \(\mathcal{CPT}\)-inner products, and pseudo-Hermiticity, Observables, disassembled, Convergent quantum normal forms, \(\mathcal PT\)-symmetry and reality of the spectrum, Stable solitons in the 1D and 2D generalized nonlinear Schrödinger equations with the periodic effective mass and \(\mathcal{PT}\)-symmetric potentials, Interaction of wave structure in the \(\mathcal{PT}\)-symmetric \((3+1)\)-dimensional nonlocal Mel'nikov equation and their applications, Bound state eigenvalues from transmission coefficients, Butterfly-shaped and dromion-like optical waves in a tapered graded-index waveguide with variable group-velocity dispersion, Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control, Dynamic behavior and stability analysis of nonlinear modes in the fourth-order generalized Ginzburg-Landau model with near \(\mathcal{PT}\)-symmetric potentials, Semiclassical calculation of the \(\mathcal C\) operator in \(\mathcal{PT}\)-symmetric quantum mechanics, Natural number dynamics: reconstructing physics from generalized atomicity, Parity-time symmetric coupled systems with varying loss/gain coefficient, Remarks on the preservation of no-signaling principle in parity-time-symmetric quantum mechanics, \({\mathcal{PT}}\)-symmetric Klein-Gordon oscillator, One- and two-dimensional gap solitons and dynamics in the \(\mathcal{PT}\)-symmetric lattice potential and spatially-periodic momentum modulation, Multi-dimensional stable fundamental solitons and excitations in \(\mathcal{PT}\)-symmetric harmonic-Gaussian potentials with unbounded gain-and-loss distributions, Localization in Matrix Computations: Theory and Applications, \(\mathcal P\mathcal T\)-symmetric quantum electrodynamics, Ghost-free higher-derivative theory, Operator equations and Moyal products-metrics in quasi-Hermitian quantum mechanics, The optical properties of two-dimensional Scarff parity-time symmetric potentials, New solutions to the \(sl_q(2)\)-invariant Yang-Baxter equations at roots of unity, An existence criterion for the \(\mathcal{PT}\)-symmetric phase transition, Nonunique \(C\) operator \(PT\) in quantum mechanics, Bragg-induced oscillations in non-\textit{PT} complex photonic lattices, Stability boundaries of a Mathieu equation having \textit{PT} symmetry, Analytically solvable PT-invariant periodic potentials, Bound state solutions of the Schrödinger equation for a \(\mathcal{PT}\)-symmetric potential with Dirac delta functions, Semi-rational solutions for the \((2 + 1)\)-dimensional nonlocal Fokas system, \(p\)-adic Schrödinger-type operator with point interactions, Recursive calculation of effective potential and variational resummation, Time-dependent PT symmetric problems, Nonlinear localized modes in \(\mathcal{PT}\)-symmetric optical media with competing gain and loss, \({\mathcal{PT}}\)-symmetric periodic optical potentials, Parity-time \((\mathcal{PT})\) invariance and pseudo-Hermitian Hamiltonian of a nonlinear oscillator, Supersymmetric quantum mechanics on non-commutative space, Quasi-Hermitian Hamiltonians, minimum-uncertainty (MU) angular momentum states and interferometers, Perpetual emulation threshold of $\mathcal{PT}$ -symmetric Hamiltonians, Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential, PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS, Lower bound of minimal time evolution in quantum mechanics, Spherical-separability of non-Hermitian Hamiltonians and pseudo-\(\mathcal{PT}\)-symmetry, On the K-theoretic classification of dynamically stable systems, ${\mathcal{PT}}$-SYMMETRIC SUPERSYMMETRY IN A SOLVABLE SHORT-RANGE MODEL, COHERENT STATES AND SCHWINGER MODELS FOR PSEUDO GENERALIZATION OF THE HEISENBERG ALGEBRA, Dirac quantization of the Pais-Uhlenbeck fourth order oscillator, Quantum dynamics of a parity-time-symmetric kicked particle in a 1D box, Faster than Hermitian Quantum Mechanics, Spatial Solitons in Parity-Time-Symmetric Photonic Lattices: Recent Theoretical Results, On the spectra of a class of PT-symmetric quantum nonlinear oscillators, Development of an approximate method for quantum optical models and their pseudo-Hermicity, Spectral problems for the Weyl-ordered form of operators $\left(\frac{1}{\hat{p}}\right)^{n} \hat{q}^{n}$1p̂nq̂n, Order-dependent mappings: Strong-coupling behavior from weak-coupling expansions in non-Hermitian theories, MHD α2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator, PT-invariant periodic potentials with a finite number of band gaps, Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)\(\mathcal{PT}\)-symmetric systems, Spectra of $\mathcal{PT}$-symmetric operators under rank-one perturbations