2014/02/28 by D. Krejcirik, David Krejčiřı́k, P. Siegl +5
Mathematics · Physics and Astronomy · #Algebra over a field #Basis (linear algebra) #Eigenfunction #Eigenvalues and eigenvectors #Geometry #Hermitian matrix #Hilbert space #Mathematical formulation of quantum mechanics #Mathematical physics #Mathematics #Operator theory #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Quantum statistical mechanics #Self-adjoint operator #Supersymmetric quantum mechanics #Symmetry in quantum mechanics #math-ph #math.MP #math.SP #quant-ph
paper · pdf · doi:10.1063/1.4934378
published as Journal of Mathematical Physics, 56, 103513 (2015) · version accepted for publication in J. Math. Phys.: criterion excluding basis property (Proposition 6) added, unbounded time-evolution discussed, new references
openalex publication_date 2015/10/01 · arxiv created 2015/11/26 · arxiv updated 2015/11/30 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
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.