Non Hermitian Operators with Real Spectrum in Quantum Mechanics

2009/09/16 by da Providência, João, Bebiano, Natália, da Providência, João Pinheiro
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.0909.3054

openalex publication_date 2009/09/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weil-Heisenberg algebra. It is argued that the existence of an involutive operator J which renders the Hamiltonian J-Hermitian leads to the unambiguous definition of an associated positive definite norm allowing for the standard probabilistic interpretation of quantum mechanics. Non-Hermitian extensions of the Poeschl-Teller Hamiltonian are also considered. Hermitian counterparts obtained by similarity transformations are constructed.

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