Pseudo-Hermiticity of Hamiltonians under imaginary shift of the co-ordinate : real spectrum of complex potentials

Details Pseudo-Hermiticity of Hamiltonians under imaginary shift of the co-ordinate : real spectrum of complex potentials Pseudo-Hermiticity of Hamiltonians under imaginary shift of the co-ordinate : real spectrum of complex potentials

2001-08-03

arxiv.org/abs/quant-ph/0108016v2

Physics

Quantum Physics

7 pages, no figure, eq.5 is changed, eqs.6a-e added, submitted to Phys. Lett. A

Scientific paper

10.1016/S0375-9601(01)00622-3

We propose that the real spectrum and the orthogonality of the states for several known complex potentials of both types, PT-symmetric and non-PT-symmetric can be understood in terms of currently proposed $\eta$-pseudo-Hermiticity (Mostafazadeh, quant-ph/0107001) of a Hamiltonian, provided the Hermitian linear automorphism, $\eta$, is introduced as $e^{-\theta p}$ which affects an imaginary shift of the co-ordinate : $e^{-\theta p} x e^{\theta p} = x+i\theta$.

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