arXiv:1705.11153

Non-Hermitian quantum mechanics of bosonic operators

Natália Bebiano João da Providência, João Pinheiro da Providência

Published May 31, 2017• 0 citations

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.

DOI: 10.48550/arxiv.1705.11153

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