ON THE PSEUDO-HERMITICITY OF A CLASS OF PT-SYMMETRIC HAMILTONIANS IN ONE DIMENSION

2002/04/30 by Ali Mostafazadeh, ALI MOSTAFAZADEH · 2 citations
Mathematics · Physics and Astronomy · #Diagonalizable matrix #Dimension (graph theory) #Hamiltonian (control theory) #Hermitian matrix #Invertible matrix #Nonlinear Waves and Solitons #Operator (biology) #Quantum Mechanics and Non-Hermitian Physics #Scalar (mathematics) #Scalar potential #Spectral Theory in Mathematical Physics #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1142/s0217732302008472

published as Mod. Phys. Lett. A 17, 1973-1977 (2002). · published version

openalex publication_date 2002/09/28 · arxiv created 2002/11/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

For a given standard Hamiltonian H = [p - A(x)] 2 /(2m) + V(x) with arbitrary complex scalar potential V and vector potential A, with x ∈ ℝ, we construct an invertible antilinear operator τ such that H is τ-anti-pseudo-hermitian, i.e. H † = τHτ -1 . We use this result to give the explicit form of a linear hermitian invertible operator with respect to which any standard PT-symmetric Hamiltonian with a real degree of freedom is pseudo-hermitian. Our results do not make use of the assumption that H is diagonalizable or that its spectrum is discrete.

Citations

• Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the coordinate: real spectrum of complex potentials

Cited by

• \mathcal P\mathcal T-symmetry, Cartan decompositions, Lie triple systems and Krein space-related Clifford algebras
• Pseudo-reality and pseudo-adjointness of Hamiltonians