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Prog. Theor. Phys. Vol. 21 No. 5 (1959) pp. 713-726
Two-Body Correlation of Interacting Fermions
Ki-ichi Nakamura
Research Laboratory, Nippon Electric Company, Limited, Kawasaki
(Received January 20, 1959)
Abstract:
The electron-pair model, proposed for superconductivity by Bardeen,
Cooper and Schrieffer, is discussed in the configuration space. The
wave function for the system of electron-pairs is taken as follows,
Ψ0 = ∑ p(-1)p Pχ(1, 2)χ(3,
4)……χ(2N-1, 2N),
where χ(1, 2) is the wave function for the singlet state of a two electron system. By a method having a remarkable similarity to Mayer's theory of an imperfect gas, the expectation value of the system can be obtained rigorously. The expression for energy coincides with that which is given by Bogoliubov in his theory of superconductivity. By a variational method, Bogoliubov's integral equation is obtained.
URL :
http://ptp.ipap.jp/link?PTP/21/713/
DOI : 10.1143/PTP.21.713
References:
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J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108 (1957), 1175[APS].
- N. N. Bogoliubov, J. Exptl. Theoret. Phys. 34 (1958), 58; Sov. Phys. 34 (1958), 41.
-
H. Fröhlich, Phys. Rev. 79 (1950), 845[APS].
J. Bardeen, Phys. Rev. 80 (1950), 567[APS].
- J. E. Mayer and M. G. Mayer, Statistical Mechanics (Wiley, 1940).
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B. Kahn and G. B. Uhlenbeck, Physica 5 (1938), 399[CrossRef].
- M. Born and K. Fuchs, Proc. Roy. Soc. London A 166 (1938), 391.
T. L. Hill, Statistical Mechanics, pp. 150-2.
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K. Yosida, Phys. Rev. 111 (1958), 1255[APS].
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L. N. Cooper, R. L. Mills and A. M. Sessler, Physica 24 (1958), S183[Elsevier].
Citing Article(s) :
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Progress of Theoretical Physics Vol. 24 No. 6 (1960) pp. 1195-1214
:
-
Cluster Expansion Technique in the Many-Fermion Systems. I
-
Ki-ichi Nakamura
-
Progress of Theoretical Physics Vol. 48 No. 1 (1972) pp. 19-30
:
-
Structure of Cooper Pairs in Superconductors
-
Yasushi Wada
