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Volume 1, Issue 1

Fermionic chain model with a non-Hermitian Hamiltonian

Pages: 30 – 40

Authors

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

Abstract

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.

Full Text (PDF format)

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