Pseudo-Hermiticity of Hamiltonians under imaginary shift of the coordinate: 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 η-pseudo-Hermiticity (A. Mostafazadeh, math-ph/0107001) of a Hamiltonian, provided the Hermitian linear automorphism, η, is introduced as e- θp which affects an imaginary shift of the coordinate: e- θpxeθp= x+ iθ.
- Publication:
-
Physics Letters A
- Pub Date:
- November 2001
- DOI:
- 10.1016/S0375-9601(01)00622-3
- arXiv:
- arXiv:quant-ph/0108016
- Bibcode:
- 2001PhLA..290...19A
- Keywords:
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- Quantum Physics
- E-Print:
- 7 pages, no figure, eq.5 is changed, eqs.6a-e added, submitted to Phys. Lett. A