On the Pseudo-Hermiticity of a Class of PT-Symmetric Hamiltonians in One Dimension

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 real, we construct an invertible antilinear operator τsuch that H is τ-anti-pseudo-Hermitian, i.e., H^\dagger=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.

published version

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• A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields
• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
• Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem
• PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras
• Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model
• Pseudo-reality and pseudo-adjointness of Hamiltonians
• On elements of the Lax-Phillips scattering scheme for PT-symmetric operators
• Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity