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

Ali Mostafazadeh
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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.

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Ali Mostafazadeh. 2002-11-07. On the Pseudo-Hermiticity of a Class of PT-Symmetric Hamiltonians in One Dimension. https://doi.org/10.1142/s0217732302008472

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