Mathematically rigorous versions of Thomas-Fermi Theory and its generalizations were developed in the 1970's and 1980's by Lieb, Simon, Benilan, Brezis, Gallouet, Morel and others. At issue is the electron density for an N electron quantum mechanical system in its ground state. The energy minimization problem is reduced to the solution of the Euler-Lagrange equation, which is reduced to the solution of a nonlinear elliptic equation in L('1) The theory which will be presented includes extensions of the existing theory to d ((GREATERTHEQ)3) dimensions and the introduction of weight functions into the kinetic energy term. Existence, nonexistence, and uniqueness results will be presented, as well as qualitative properties of the solutions / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_23098 |
| Date | January 1986 |
| Contributors | Rieder, Gisele Ruiz (Author) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Rights | Access requires a license to the Dissertations and Theses (ProQuest) database., Copyright is in accordance with U.S. Copyright law |
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