Numerical ranges of unbounded operators arising in quantum physics

Abstract

Creation and annihilation operators are used in quantum physics as the building blocks of linear operators acting on Hilbert spaces of many body systems. In quantum physics, pairing operators are defined in terms of those operators. In this paper, spectral properties of pairing operators are studied. The numerical ranges of pairing operators are investigated. In the context of matrix theory, the results give the numerical ranges of certain infinite tridiagonal matrices.