DOI: 10.1098/rsta.1938.0004. The computation of Fermi-Dirac functions

The computation of Fermi-Dirac functions

10.1098/rsta.1938.0004

Crossref journal-article

The Royal Society

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences (175)

Abstract

The quantitative application of Fermi-Dirac statistics involves the evaluation of certain integrals which have not previously been tabulated. In this paper, tables are given of the values of the basic integrals most frequently required , with a view to placing Fermi-Dirrac statistics on as firm a numerical basis as is Maxwell-Boltzmann statistics. T e expression for the energy distribution of particles subject to Fermi-Dirrac statistics may be written in the form dN He) de e<*+Pe -)-1 ’ wherev(e) is the number of states per unit energy range, and dN is the number of particles in the energy range e to e--de. In the statistical treatment, the parameters ot and fi, which are usually introduced as undetermined multipliers in a variational equation, are to be determined from two equations expressing conditions imposed by the total number of particles, and the total energy of the system. By linking up the statistical and thermodynamical treatments, interpretation can be given to a and b this is expressed by P**:l IkT, a = -C lk T ,

Bibliography

The computation of Fermi-Dirac functions. (1938). Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 237(773), 67â104.

Authors 0

None

References 12 Referenced 328

Becker G. F. and van Orstrand C. E. 1909 " Hyperbolic Functions." Smithsonian Instn Publ.
Gomrie L. J. (ed.) 1935 " Barlow's Tables." London: Spon. - 1936 " Interpolation and Allied Tables." Reprinted from the- 1937. H.M. Stationery Office.
{'key': 'p_3', 'first-page': '313', 'article-title': 'K.Danske Vidensk', 'volume': '10', 'author': 'Gram J. P.', 'year': '1925', 'journal-title': 'Selsk. Skr.'} / Selsk. Skr. / K.Danske Vidensk by Gram J. P. (1925)
{'key': 'p_4', 'first-page': '243', 'volume': '13', 'author': 'Glaisher J. W. L.', 'year': '1883', 'journal-title': 'Trans. Camb. Phil. Soc.'} / Trans. Camb. Phil. Soc. by Glaisher J. W. L. (1883)
{'key': 'p_5', 'first-page': '117', 'article-title': 'Proc', 'volume': '3', 'author': 'Gilliam G. W.', 'year': '1936', 'journal-title': 'Leeds Phil. Soc.'} / Leeds Phil. Soc. / Proc by Gilliam G. W. (1936)
Jahnke E. and Emde F. 1933 " Funktionentafeln mit Formeln und Kurven." Leipzig: Teubner.
{'key': 'p_7', 'first-page': '145', 'volume': '13', 'author': 'Newman F. W.', 'year': '1883', 'journal-title': 'Trans. Camb. Phil. Soc.'} / Trans. Camb. Phil. Soc. by Newman F. W. (1883)
Nordheim L. 1934 " Muller Pouillets Lehrbuch der Physik" 4 4 277. Braunschweig.
{'key': 'p_9', 'first-page': '672', 'article-title': 'Proc. Roy', 'volume': '152', 'author': 'Stoner E. C.', 'year': '1935', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Stoner E. C. (1935)
Sommerfeld A. 1928 Z.Phys. 47 1. (10.1007/BF01391055)
Whittaker E. T. and Watson G. N. 1935 " Modern Analysis." Camb. Univ. Press.
Whittaker E. T. and Robinson G. 1932 " The Calculus of Observations." London: Blackie.

Dates

Type	When
Created	18 years, 8 months ago (Dec. 15, 2006, 1:02 p.m.)
Deposited	4 years, 6 months ago (Feb. 14, 2021, 5:39 a.m.)
Indexed	1 month, 3 weeks ago (July 11, 2025, 9:11 p.m.)
Issued	87 years, 6 months ago (Feb. 7, 1938)
Published	87 years, 6 months ago (Feb. 7, 1938)
Published Online	28 years, 8 months ago (Jan. 1, 1997)
Published Print	87 years, 6 months ago (Feb. 7, 1938)

Funders 0

None

BibTeX

@article{1938, volume={237}, ISSN={2054-0272}, url={http://dx.doi.org/10.1098/rsta.1938.0004}, DOI={10.1098/rsta.1938.0004}, number={773}, journal={Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences}, publisher={The Royal Society}, year={1938}, month=feb, pages={67–104} }

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