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Nonstandard pertubation methods and non-Hermitian models in quantum mechanics
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SYSNO ASEP 0557364 Document Type D - Thesis R&D Document Type The record was not marked in the RIV Title Nonstandard pertubation methods and non-Hermitian models in quantum mechanics Author(s) Semorádová, Iveta (UJF-V) ORCID, SAI Number of authors 1 Issue data Praha, 2021 Number of pages 126 s. Publication form Print - P Language eng - English Country CZ - Czech Republic Keywords quantum mechanics ; non-self-adjoint Schrödinger operator ; quasi-Hermitian observables ; domain truncation ; diverging eigenvalues ; spectral approximation OECD category Pure mathematics Institutional support UJF-V - RVO:61389005 Annotation This thesis is devoted to investigation of the spectra of Schr¨odinger operators H = −∆ + Q(x), L2(Ω) with Ω ⊂ Rd open, Dirichlet boundary conditions at ∂Ω and Q : Ω → C.
We study quantum mechanics with self-adjoint, quasi-self-adjoint and nonself-adjoint observables H. Perturbation theory and spectral approximations are the main tools used in this thesis. The approximating operators may differ in both potential and domain. Asymptotic formulae for eigenvalues are derived and proven to be true for various problems with strong coupling Q(x, g), g → ∞ and for diverging eigenvalues occuring in domain truncations of Schröodinger operators with complex potential.
Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2023
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