Absence of a Scott Correction for the Total Binding Energy of Noninteracting Fermions in a Smooth Potential Well

Atomic physics;quantum mechanics;Scott correction;semi-classical approximation;Thomas-Fermi theory

Huxtable, Barton Duane ; Simon, Barry M.

University:California Institute of Technology

Department:Physics, Mathematics and Astronomy

关键词: Atomic physics;    quantum mechanics;    Scott correction;    semi-classical approximation;    Thomas-Fermi theory;   

Others  :  https://thesis.library.caltech.edu/3349/11/huxtable_bd_1988.pdf

美国|英语

来源: Caltech THESIS

【 摘 要 】

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 Z^4/3V(Z^1/3x), obeys E(Z) = c_TF(V)Z^7/3 + 0(Z^5/3) as Z → ∞. Here c_TF(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.