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

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

2002-04-08

arxiv.org/abs/math-ph/0204013v3

Mod. Phys. Lett. A 17, 1973-1977 (2002).

Physics

Mathematical Physics

published version

Scientific paper

10.1142/S0217732302008472

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 \tau such that H is \tau-anti-pseudo-Hermitian, i.e., H^\dagger=\tau H\tau^{-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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