Pseudospectra in non-Hermitian quantum mechanics
Spectral Theory
2015-11-30 v2 Mathematical Physics
math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.1402.1082,
title = {Pseudospectra in non-Hermitian quantum mechanics},
author = {D. Krejcirik and P. Siegl and M. Tater and J. Viola},
journal= {arXiv preprint arXiv:1402.1082},
year = {2015}
}
Comments
version accepted for publication in J. Math. Phys.: criterion excluding basis property (Proposition 6) added, unbounded time-evolution discussed, new references