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Calculus of variations in quantum mechanics
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Capet, Stéphane (2006) Calculus of variations in quantum mechanics. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3781734
Abstract
We marginally improve the bound of Lieb on the stability of ions i.e. we show that Nc < 2Z + 1 — f(Z) with f(Z) > 0 explicitly given. Then, we study the existence of a ground state for a classical model derived from the Ar-body Hamiltonian operator. We establish amongst other things that the A-body Coulomb potential does not favour shell formation. We also expose some properties related to the screening effect and conjecture, using numerical data, that the negative ionization charge is unbounded as the nuclear charge grows to infinity. In joint work with my supervisor, we study the ground state of the model just described as A tends to infinity. We show that our model Gamma-converges toward a Gamma-limit. We derive from it an angular equidistribution law, a radial condensation law, and the asymptotic neutrality of the crossover point from attainment and non-attainment. Finally we prove the existence of a minimizer for hydrogen Kolm-Sham functional if A < Z. More generally we show existence of a minimizer for the Kohn-Sham functional in the case A < Z without taking into account the orthogonality condition between orbitals.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Library of Congress Subject Headings (LCSH): | Quantum theory, Particles (Nuclear physics) -- Mathematical models, Density functionals | ||||
Official Date: | September 2006 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Friesecke, Gero | ||||
Sponsors: | University of Warwick ; Engineering and Physical Sciences Research Council ; Technische Universität München | ||||
Format of File: | |||||
Extent: | ix, 139 pages | ||||
Language: | eng |
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