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On the pseudo-hermiticity of a class of PT-symmetric Hamiltonians in one dimension

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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.

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World Scientific Publ Co Pte Ltd

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Astronomy, Astrophysics, Physics, nuclear, Physics, particles and fields, Physics, mathematical

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Modern Physics Letters A

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10.1142/S0217732302008472

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