Pseudo-reality and pseudo-adjointness of Hamiltonians

2003/06/13 by Zafar Ahmed
Mathematics · Physics and Astronomy · #Adiabatic quantum computation #Algebraic and Geometric Analysis #Hamiltonian (control theory) #Operator (biology) #Operator matrix #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #Spectrum (functional analysis) #quant-ph

paper · pdf · doi:10.1088/0305-4470/36/41/005

No Figures, 11 pages

arxiv created 2003/06/13 · openalex publication_date 2003/10/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We define pseudo-reality and pseudo-adjointness of a Hamiltonian, H , as ρ H ρ −1 = H * and μ H μ −1 = H ', respectively. We prove that the former yields the necessary condition for a spectrum to be real whereas the latter helps in fixing a definition for the inner-product of the eigenstates. Here we separate out the adjointness of an operator from its Hermitian adjointness. It turns out that a Hamiltonian possessing a real spectrum is first pseudo-real, further it could be Hermitian, PT -symmetric or pseudo-Hermitian.

Citations

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