Citation
Huxtable, Barton Duane (1988) Absence of a Scott Correction for the Total Binding Energy of Noninteracting Fermions in a Smooth Potential Well. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/87FQ-5X29. https://resolver.caltech.edu/CaltechETD:etd-09062005-101909
Abstract
It is shown, for V in a particular class of smooth functions, that the total binding energy, E(Z), of Z noninteracting Fermions in the potential well Z4/3V(Z1/3x), obeys E(Z) = cTF(V)Z7/3 + 0(Z5/3) as Z → ∞. Here cTF(V) is the coefficient predicted by the Thomas-Fermi theory. This result is consistent with the conjectured Scott correction, which occurs at order Z2, to the total binding energy of an atom of atomic number Z. This correction is thought to arise only because V(x) ~ - |x|1 near x - 0 in the atomic problem, and so V is not a smooth function.
| Item Type: | Thesis (Dissertation (Ph.D.)) | ||||||||
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| Subject Keywords: | Atomic physics; quantum mechanics; Scott correction; semi-classical approximation; Thomas-Fermi theory | ||||||||
| Degree Grantor: | California Institute of Technology | ||||||||
| Division: | Physics, Mathematics and Astronomy | ||||||||
| Major Option: | Physics | ||||||||
| Thesis Availability: | Public (worldwide access) | ||||||||
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| Defense Date: | 16 June 1987 | ||||||||
| Non-Caltech Author Email: | bhuxtable (AT) usersystems.com | ||||||||
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| Record Number: | CaltechETD:etd-09062005-101909 | ||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechETD:etd-09062005-101909 | ||||||||
| DOI: | 10.7907/87FQ-5X29 | ||||||||
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
| ID Code: | 3349 | ||||||||
| Collection: | CaltechTHESIS | ||||||||
| Deposited By: | Imported from ETD-db | ||||||||
| Deposited On: | 06 Sep 2005 | ||||||||
| Last Modified: | 29 Jan 2020 01:18 |
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