Conta, Verena von (2015): Statistical theory of the atom in momentum space. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics 

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Abstract
In 1992, Englert [Phys. Rev. A, 45;127134] found a momentum energy functional for atoms and discussed the relation to the ThomasFermi functional (Lenz [Z. Phys., 77;713721]). We place this model in a mathematical setting. Our results include a proof of existence and uniqueness of a minimizing momentum density for this momentum energy functional. Further, we investigate some properties of this minimizer, among them the connection with Euler's equation. We relate the minimizers of the ThomasFermi functional and the momentum energy functional found by Englert by explicit transforms. It turns out that in this way results wellknown in the ThomasFermi model can be transferred directly to the model under consideration. In fact, we gain equivalence of the two functionals upon minimization. Finally, we consider momentum dependent perturbations. In particular, we show that the atomic momentum density converges to the minimizer of the momentum energy functional as the total nuclear charge becomes large in a certain sense. This thesis is based on joint work with Prof. Dr. Heinz Siedentop and the main contents will also appear in a joint article.
Item Type:  Theses (Dissertation, LMU Munich) 

Keywords:  statistical theory in momentum space, asymptptic behavior of the momentum density 
Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 510 Mathematics 
Faculties:  Faculty of Mathematics, Computer Science and Statistics 
Language:  English 
Date of oral examination:  13. April 2015 
1. Referee:  Siedentop, Heinz 
MD5 Checksum of the PDFfile:  3802a6966c9e4640aaad4caa2632b4d1 
Signature of the printed copy:  0001/UMC 23232 
ID Code:  18695 
Deposited On:  23. Sep 2015 07:30 
Last Modified:  23. Oct 2020 21:36 