Non self-adjoint operators with real spectra and extensions of quantum mechanics (Preprint)

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Type: Preprint
National /International: International
Title: Non self-adjoint operators with real spectra and extensions of quantum mechanics
Publication Date: 2018-12-12
Authors: - Natália Bebiano
- João da Providência
Abstract: In this article, we review the quantum mechanical setting associated to a non self-adjoint Hamiltonian with a real spectrum. Spectral properties of the Hamiltonian of a Swanson-like model are investigated. The eigenfunctions associated to the real simple eigenvalues are shown to form complete systems but not a (Riesz) basis, which gives rise to difficulties in the rigorous mathematical formulation of quantum mechanics. A new inner product, appropriate for the physical interpretation of the model, has been consistently introduced. The dynamics of the system is described. Some specificities of the theory of non self-adjoint operators with implications in quantum mechanics are discussed.
Institution: DMUC 18-57
Online version: http://www.mat.uc.pt...prints/eng_2018.html
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