We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.
|Journal||Journal of Mathematical Physics|
|Publication status||Published - 1 Oct 2015|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics