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Pseudospectra in non-Hermitian quantum mechanics

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arxiv 1402.1082 v2 pith:ZBTJUY5P submitted 2014-02-05 math.SP math-phmath.MPquant-ph

Pseudospectra in non-Hermitian quantum mechanics

D. Krejcirik , P. Siegl , M. Tater , J. Viola This is my paper
classification math.SP math-phmath.MPquant-ph
keywords mechanicsoperatorspropertiesquantumnon-hermitianabstractbasiscentral
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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