Majorana solution of the Thomas-Fermi equation

American Journal of Physics

Volumn 70, Issue 8, 2002, Pages 852-856

  Esposito, Salvatore ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141469696     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1484144     Document Type: Article

References (12)

1. B. H. Bransden and C. J. Joachain, Physics of Atoms and Molecules (Longman, London, 1995);
2. N. H. March, Self-Consistent Fields in Atoms (Pergamon, Oxford, 1975);
3. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford U.P., New York, 1989).
4. L. H. Thomas, "The calculations of atomic fields," Proc. Cambridge Phi-los. Soc. 23, 542-598 (1927);
5. E. Fermi, "Eine statistiche Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente," Z. Phys. 48, 73-79 (1928).
6. L. Spruch, "Pedagogic notes on Thomas-Fermi theory (and on some improvements): Atoms, stars and the stability of bulk matter," Rev. Mod. Phys. 63, 151-209 (1991).
7. S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs and Neutron Stars (Wiley, New York, 1983).
8. A. Sommerfeld, "Integrazione asintotica dell'equazione differenziale di Thomas-Fermi," Rend. R. Accademia dei Lincei 15, 293-308 (1932).
9. S. Esposito, E. Majorana, Jr., A. van der Merwe, and E. Recami, Errore Majorana: Notebooks in Theoretical Physics (Kluwer, New York, to be published).
10. L. N. Epele, H. Fanchiotti, C. A. Garcia Canal, and J. A. Ponciano, "Padé approximant approach to the Thomas-Fermi problem," Phys. Rev. A 60, 280-283 (1999).
11. Equation (42) is, probably, the major result of this paper and was obtained by Majorana. What follows is an original further elaboration of the material presented above.
12. For simplicity, we also assume that all the zeros of Q(T) are simple roots, as is likely in the present case. The generalization to the case in which multiple roots are present is straightforward.