arXiv:math-ph/0204013 · Modern Physics Letters A

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

ALI MOSTAFAZADEH

Published Sep 28, 2002• 24 citations

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.

DOI: 10.1142/s0217732302008472

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