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

2001/08/10 by Zafar Ahmed · 5 citations
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #quant-ph

paper · pdf · doi:10.1016/s0375-9601(01)00622-3

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

arxiv created 2001/08/10 · openalex publication_date 2001/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (Mostafazadeh, quant-ph/0107001) of a Hamiltonian, provided the Hermitian linear automorphism, η, is introduced as e^-θp which affects an imaginary shift of the co-ordinate : e^-θp x e^θp = x+iθ.

Cited by

• On the real spectra of the Calogero model with complex coupling
• Pseudounitary symmetry and the Gaussian pseudounitary ensemble of random matrices
• SUPERSYMMETRIC SOLUTION OF PT-/NON-PT-SYMMETRIC AND NON-HERMITIAN MORSE POTENTIAL VIA HAMILTONIAN HIERARCHY METHOD
• Pseudo-Hermiticity and some consequences of a generalized quantum condition
• Shape invariance approach to exact solutions of the Klein–Gordon equation