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Volume 1, Issue 1

Fermionic chain model with a non-Hermitian Hamiltonian

Pages: 30 – 40


N. Bebiano, J. da Providência and J.P. da Providência


This article deals with the quantum mechanical setting of a fermionic system associated to a non-Hermitian Hamiltonian with real eigenvalues. Spectral properties of the Hamiltonian and of its adjoint are studied and their eigenfunctions are shown to form biorthogonal systems.The difficulties originated by non-Hermicity in the development of a mathematically rigorous and physically consistent quantum theory are investigated. A new inner product, appropriate for the physical interpretation of the model, is consistently introduced in the Hilbert space where the Hamiltonian acts. The dynamics of the system is described.

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Received: 10 April 2019; Accepted: 21 June 2019.