Convergence of the Series Expansion Solution to the Thomas–Fermi–Dirac Equation

1971 ◽  
Vol 54 (2) ◽  
pp. 820-822
Author(s):  
James E. Enstrom
Keyword(s):  
Dirac Equation ◽  
Series Expansion ◽  
Thomas Fermi

scholarly journals Numerical Calculation of the Electron Density at the Wigner–Seitz Radius Based on the Thomas–Fermi–Dirac Equation

2014 ◽  
Vol 11 (2) ◽  
pp. 344-347 ◽  
Author(s):  
Fengzhang Ren ◽  
Ke Cao ◽  
Jiangzhuo Ren ◽  
Alex A. Volinsky ◽  
Thanh Hai Tran ◽  
...  
Keyword(s):  
Numerical Calculation ◽  
Dirac Equation ◽  
Electron Density ◽  
Thomas Fermi

scholarly journals Solution of the Thomas-Fermi-Dirac Equation

Nature ◽  
1951 ◽  
Vol 168 (4264) ◽  
pp. 122-122 ◽  
Author(s):  
P. GOMBÁS ◽  
R. GÁSPÁR
Keyword(s):  
Dirac Equation ◽  
Thomas Fermi

Effect of Quantum Inhomogeneity Corrections in Semi-Statistical Thomas–Fermi Calculations for Atoms

1974 ◽  
Vol 52 (19) ◽  
pp. 1926-1932 ◽  
Author(s):  
J. A. Stauffer ◽  
J. W. Darewych
Keyword(s):  
Dirac Equation ◽  
Variational Method ◽  
Quantum Correction ◽  
Correction Term ◽  
Approximate Solutions ◽  
The Other ◽  
Gradient Term ◽  
Gradient Expansion ◽  
Thomas Fermi ◽  
Correction Terms

Approximate solutions to the Thomas–Fermi equation with so-called 'quantum correction terms' have been obtained by the use of a variational method. The results for krypton support the conclusions of Tomishima and Yonei that the coefficient of the gradient term should be 9/5 of the value derived by Kirzhnits. On the other hand, when the use of these equations is restricted to a region of the atom where the gradient expansion of Kirzhnits might be expected to be valid, the Kirzhnits value of the constant gives the better results, but the best results are obtained with no correction term at all (i.e. with the Thomas–Fermi–Dirac equation).

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