scholarly journals APPLICATIONS OF A FULLY VARIATIONAL METHOD FOR SOLVING ZERO ORDER THOMAS-FERMI EQUATIONS

1984 ◽  
Vol 45 (C6) ◽  
pp. C6-161-C6-166
Author(s):  
E. Suraud
Keyword(s):  
Variational Method ◽  
Zero Order ◽  
Thomas Fermi

Angular terms in the electron density for the phosphine molecule

1956 ◽  
Vol 52 (4) ◽  
pp. 703-711 ◽  
Author(s):  
R. A. Ballinger ◽  
N. H. March
Keyword(s):  
Variational Method ◽  
Charge Density ◽  
Electron Density ◽  
Legendre Polynomials ◽  
Molecular Axis ◽  
Thomas Fermi ◽  
Line Charge ◽  
Density Map ◽  
Circular Line

ABSTRACTAn attempt is made to calculate the first few angular terms in an expansion of the electron density for the phosphine molecule in Legendre polynomials. Such an expansion is appropriate for a model in which the three hydrogen nuclei are smeared to form a circular line charge. The Thomas–Fermi approximation has been used in conjunction with the variational method. The variational density employed includes p and f angular terms. An approximate charge density map is constructed for a plane containing the molecular axis in order to demonstrate the effect of the angular terms.

The application of variational methods to atomic scattering problems III. The elastic scattering of electrons by helium atoms

1953 ◽  
Vol 219 (1136) ◽  
pp. 102-109 ◽  
Keyword(s):  
Differential Equation ◽  
Wave Function ◽  
Elastic Scattering ◽  
Phase Shift ◽  
Variational Method ◽  
Zero Order ◽  
Scattering Problems ◽  
Helium Atoms ◽  
Atomic Scattering ◽  
Slow Electrons

The variational method of Hulthèn has been applied to the elastic scattering of slow electrons by helium atoms, the effect of exchange being taken into account in calculating the zero-order phase shift. Satisfactory agreement has been obtained with the results given by numerical integration of the integro-differential equation determining the scattering when the total wave function is taken to be completely antisymmetric. Even at very low electron energies (0·04 eV) the agreement with experiment is good.

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).

Statistical theory of electron densities: multiple scattering perturbation theory

1991 ◽  
Vol 435 (1894) ◽  
pp. 245-255 ◽  
Keyword(s):  
Perturbation Theory ◽  
Multiple Scattering ◽  
Electron Density ◽  
Energy Scale ◽  
Zero Order ◽  
Fermi Theory ◽  
Electron Densities ◽  
Thomas Fermi ◽  
Order Contribution ◽  
Explicit Formulae

A multiple scattering perturbation theory for electron densities, originally discussed by N. H. March and A. M. Murray, is derived in a new way. The new derivation does not depend on special choices for the origin of the energy scale. Therefore, it clarifies the point that the result of the perturbation calculation, the electron density, should be independent of the energy origin chosen for the purposes of the calculation even though the individual terms of the series do depend on that choice. This point is not evident in the previous derivations. Appreciation of this point permits adoption of an origin of the energy scale which varies with position without any change in form of the perturbation expansion. This extends the original theory beyond the significant limitation that the zero-order result is the uniform density of the free-electron gas. In particular, the energy origin can be chosen so that the zero-order contribution reproduces any physical model electron density. The theory then gives successive corrections and allows investigation of the usefulness of physical models by an analysis of the low-order corrections. These ideas permit a compact new derivation of the Thomas–Fermi theory, a derivation which also produces explicit formulae for corrections of all orders. An especially useful choice for the energy origin yields the optimized Thomas–Fermi theory as the zero-order contribution. Therefore, new results of this development are explicit formulae for the corrections to that simple theory.

scholarly journals Nonuniform Matter in Neutron Star Crusts Studied by the Variational Method with Thomas-Fermi Calculations

2009 ◽  
Vol 122 (3) ◽  
pp. 673-691 ◽  
Author(s):  
H. Kanzawa ◽  
M. Takano ◽  
K. Oyamatsu ◽  
K. Sumiyoshi
Keyword(s):  
Neutron Star ◽  
Variational Method ◽  
Thomas Fermi

Strain measurement in In0.2Ga0.8As/GaAs quantum wires by convergent beam electron diffraction

1995 ◽  
Vol 53 ◽  
pp. 444-445
Author(s):  
S. Hillyard ◽  
Y.-P. Chen ◽  
J.D. Reed ◽  
W.J. Schaff ◽  
L.F. Eastman ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Semiconductor Lasers ◽  
Quantum Wire ◽  
Quantum Wires ◽  
Convergent Beam Electron Diffraction ◽  
Zero Order ◽  
Beam Electron ◽  
Local Lattice ◽  
Device Applications ◽  
Convergent Beam

The positions of high-order Laue zone (HOLZ) lines in the zero order disc of convergent beam electron diffraction (CBED) patterns are extremely sensitive to local lattice parameters. With proper care, these can be measured to a level of one part in 104 in nanometer sized areas. Recent upgrades to the Cornell UHV STEM have made energy filtered CBED possible with a slow scan CCD, and this technique has been applied to the measurement of strain in In0.2Ga0.8 As wires.Semiconductor quantum wire structures have attracted much interest for potential device applications. For example, semiconductor lasers with quantum wires should exhibit an improvement in performance over quantum well counterparts. Strained quantum wires are expected to have even better performance. However, not much is known about the true behavior of strain in actual structures, a parameter critical to their performance.

Study on Discrete Autonomous Traffic Flow Model with Zero-Order Hold

CICTP 2020 ◽  
2020 ◽  
Author(s):  
Lidong Zhang ◽  
Wenxing Zhu ◽  
Mengmeng Zhang ◽  
Cuijiao Chen
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Zero Order ◽  
Traffic Flow Model
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