Nonstandard pertubation methods and non-Hermitian models in quantum mechanics

0557364 - ÚJF 2023 CZ eng D - Thesis
Semorádová, Iveta
Nonstandard pertubation methods and non-Hermitian models in quantum mechanics.
Ústav jaderné fyziky AV ČR. Defended: Fakulta jaderná a fyzikálně inženýrská, Katedra fyziky, ČVUT. 11. 10. 2022. - Praha, 2021. 126 s.
Institutional support: RVO:61389005
Keywords : quantum mechanics * non-self-adjoint Schrödinger operator * quasi-Hermitian observables * domain truncation * diverging eigenvalues * spectral approximation
OECD category: Pure mathematics
https://www.fjfi.cvut.cz/cz/studium/doktorske-studium/archiv-doktorskych-praci/1029-semoradova-iveta

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.

Permanent Link: http://hdl.handle.net/11104/0331408