Non-Hermitian quantum mechanics of bosonic operators
Quantum Physics
2017-06-01 v1 Mathematical Physics
math.MP
Abstract
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral instabilities. We demonstrate that the considered operator and its adjoint can be diagonalized when expressed in terms of certain conveniently constructed operators. We show that their eigenfunctions constitute complete systems, but do not form Riesz bases. Attempts to overcome this difficulty in the quantum mechanical set up are pointed out.
Keywords
Cite
@article{arxiv.1705.11153,
title = {Non-Hermitian quantum mechanics of bosonic operators},
author = {Natália Bebiano João da Providência and João Pinheiro da Providência},
journal= {arXiv preprint arXiv:1705.11153},
year = {2017}
}