Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians

Abstract

We give a simple proof of the fact that every diagonalizable operator that has a real spectrum is quasi-Hermitian and show how the metric operators associated with a quasi-Hermitian Hamiltonian are related to the symmetry generators of an equivalent Hermitian Hamiltonian.

arXiv comment6 pages, published version

References in corpus (15)

• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Exact PT-Symmetry Is Equivalent to Hermiticity
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• Time evolution of non-Hermitian Hamiltonian systems
• Metric Operator in Pseudo-Hermitian Quantum Mechanics and the Imaginary Cubic Potential
• Operator equations and Moyal products -- metrics in quasi-hermitian quantum mechanics
• PT-Symmetric Quantum Mechanics: A Precise and Consistent Formulation
• Isospectral Hamiltonians from Moyal products
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation

Cited by in corpus (16)

• A spin chain model with non-Hermitian interaction: The Ising quantum spin chain in an imaginary field
• The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes
• Application of Pseudo-Hermitian Quantum Mechanics to a Complex Scattering Potential with Point Interactions
• Non-Hermitian Chiral Magnetic Effect in Equilibrium
• Exceptional points in oligomer chains
• $\mathcal{D}$-deformed harmonic oscillators
• Dynamical control of solitons in a parity-time-symmetric coupler by periodic management
• Hilbert space inner products for PT-symmetric Su-Schrieffer-Heeger models
• Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories
• Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems
• Non-local PT-symmetric potentials in the one-dimensional Dirac equation
• Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators
• Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity
• Nonlocality of Observables in Quasi-Hermitian Quantum Theory
• Swanson Hamiltonian: non-PT-symmetry phase
• Infinite series of time-dependent Dyson maps