<Reference List> | |
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 |
Download: | Not available |