Pseudospectra in non-Hermitian quantum mechanics
arXiv:1402.1082 · doi:10.1063/1.4934378
Abstract
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.
version accepted for publication in J. Math. Phys.: criterion excluding basis property (Proposition 6) added, unbounded time-evolution discussed, new references