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

Abstract

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 : $e^{-\theta p}x{e}^{\theta p}=x+i\theta$.

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

References in corpus (2)

• Conservation of pseudo-norm in PT symmetric quantum mechanics
• The Interpretation of Quantum-Mechanical Models with Non-Hermitian Hamiltonians and Real Spectra

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