Department of Mathematics2024-11-0920020217-732310.1142/S02177323020084722-s2.0-0037190620http://dx.doi.org/10.1142/S0217732302008472https://hdl.handle.net/20.500.14288/14016For 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.AstronomyAstrophysicsPhysics, nuclearPhysics, particles and fieldsPhysics, mathematicalJournal Article179206300004Q212997