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Chin. Phys. B, 2013, Vol. 22(8): 087101    DOI: 10.1088/1674-1056/22/8/087101
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

Some corrections to the Thomas–Fermi theory

Janusz Chrzanowski
Institute of Physics, Maritime University of Szczecin, 1-2 Waly Chrobrego, Szczecin 70-500, Poland
Abstract  In the presented model the wave function describing the electron is a superposition of contributions from individual components of the system, in the case of metals–lattice ions and in this sense refers not to a single electron, but rather to the system as a whole. An unconventional approach to the Schrödinger equation can provide a simple analytical relationship between the total energy of the electron and the wave number. This expression can directly determine the basic parameters such as Fermi radius, the screening radius or work function and also produce a graphical interpretation of the Fermi surface.
Keywords:  screening parameter      convolution      Fermi surface  
Received:  12 November 2012      Revised:  03 January 2013      Accepted manuscript online: 
PACS:  71.10.Ca (Electron gas, Fermi gas)  
  71.15.Nc (Total energy and cohesive energy calculations)  
  71.18.+y (Fermi surface: calculations and measurements; effective mass, g factor)  
  73.30.+y (Surface double layers, Schottky barriers, and work functions)  
Corresponding Authors:  Janusz Chrzanowski     E-mail:  j.chrzanowski@am.szczecin.pl

Cite this article: 

Janusz Chrzanowski Some corrections to the Thomas–Fermi theory 2013 Chin. Phys. B 22 087101

[1] Bendtsen C, Nielsen O and Hansen L 2001 Appl. Numer. Math. 37 189
[2] Singh D 1989 Phys. Rev. B 40 5428
[3] Wang L W and Teter M P 1992 Phys. Rev. B 45 13196
[4] Teller E 1962 Rev. Mod. Phys. 34 627
[5] Hohenberg P and Kohn W 1964 Phys. Rev. 136 (3B) B864
[6] Burke K, Werschnik J and Gross E K U 2005 J. Chem. Phys. 123 062206
[7] Kohn W and Sham L J 1965 Phys. Rev. 140 (4A) A1133
[8] Ceperley D M and Alder B J 1980 Phys. Rev. Lett. 45 566
[9] Newman M E J and Barkema G T 1999 Monte Carlo Methods in Statistical Physics (Oxford: Oxford University Press)
[10] Filippi C and Ceperley D M 1999 Phys. Rev. B 59 7907
[11] Lin L, Lu J, Ying L and Weinan E 2011 J. Comput. Phys. 45 15
[12] Gong S and Liu B G 2012 Chin. Phys. B 21 057104
[13] Hartree D R 1927 Proc. Camb. Phil. Soc. 106 89
[14] Seifert G and Eschrig H 1985 Phys. Status Solidi 127 529
[15] Bersuker I B 2010 Electronic Structure and Properties of Transition Metal Compounds (New Jersey: John Willey and Sons)
[16] Ashcroft N W and Mermin N D 1976 Solid State Physics (New York: Holt Rinehart and Winston)
[17] Harrison W A 1989 Electronic Structure and the Properties of Solids (New York: Dover)
[18] Bracewell R 2000 Fourier Transform and Its Application (New Yourk: Mc Graw-Hill)
[19] Chrzanowski J 2003 Opt. Appl. 33 457
[20] Chrzanowski J and Kravtsov Yu A 2011 Phys. Lett. A 375 671
[21] Abrikosow A 1998 Fundamentals of the Theory of Metals (Amsterdam: North Holland)
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