Pseudomodes for Schrödinger operators with complex potentials

David Krejčiřík, Petr Siegl

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For one-dimensional Schrödinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. We develop a first systematic non-semi-classical approach, which results in a substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials, including discontinuous ones. Applications of the present results to higher-dimensional Schrödinger operators are also discussed.
Original languageEnglish
Pages (from-to)2856
JournalJournal of Functional Analysis
Issue number9
Early online date10 Oct 2018
Publication statusEarly online date - 10 Oct 2018


  • Pseudospectrum, Schrödinger operators, Complex potential, WKB

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