Abstract
In second quantization, the characteristic properties of eigenfunctions are transferred to operators. This approach has the advantage of treating the atomic shell as the basic unit, as opposed to the electron configuration. The creation and annihilation operators allow one to move from configuration to configuration, exposing an intrinsic shell structure. The introduction of coefficients of fractional parentage (cfp) then allows the calculation of the matrix elements of an operator in one configuration to be expressed in terms of those of the same operator in another configuration; hence the matrix elements of an operator in all configurations may be determined from the knowledge of its matrix elements in but one. This can be viewed as an extension of the usual Wigner-Eckart theorem. The basic concepts of quasispin and quasiparticle are also introduced within this context.
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References
E. K. U. Gross, E. Runge, O. Heinonen: Many-Particle Theory (Hilger, New York 1991)
G. Racah: Phys. Rev. 62, 438 (1942)
E. U. Condon, G. H. Shortley: The Theory of Atomic Spectra (Cambridge Univ. Press, New York 1935)
A. R. Edmonds: Angular Momentum in Quantum Mechanics (Princeton Univ. Press, Princeton 1957)
C. W. Nielson, G. F. Koster: Spectroscopic Coefficients for the p n , d n , and f n Configurations (MIT Press, Cambridge 1963)
R. Karazija, J. Vizbaraitė, Z. Rudzikas, A. P. Jucys: Tables for the Calculation of Matrix Elements of Atomic Operators (Academy Sci. Computing Center, Moscow 1967)
B. R. Judd: Second Quantization and Atomic Spectroscopy (Johns Hopkins, Baltimore 1967)
G. Racah: Phys. Rev. 63, 367 (1943)
V. L. Donlan: Air Force Materials Laboratory Report No. AFML-TR-70-249 (Wright-Patterson Air Force Base, Ohio 1970)
D. D. Velkov: Multi-Electron Coefficients of Fractional Parentage for the p, d, and f Shells. Ph.D. Thesis (The Johns Hopkins University, Baltimore 2000) http://www.pha.jhu.edu/groups/cfp/
P. J. Redmond: Proc. R. Soc. London A222, 84 (1954)
B. H. Flowers, S. Szpikowski: Proc. Phys. Soc. London 84, 673 (1964)
Z. Rudzikas: Theoretical Atomic Spectroscopy (Cambridge Univ. Press, New York 1997)
G. Gaigalas, Z. Rudzikas, C. Froese Fischer: At. Data Nucl. Data Tables 70, 1 (1998)
B. R. Judd, E. Lo, D. Velkov: Mol. Phys. 98, 1151 (2000), Table 4
B. R. Judd: J. Phys. C 14, 375 (1981)
J. S. Bell: Nucl. Phys. 12, 117 (1959)
H. Watanabe: Prog. Theor. Phys. 32, 106 (1964)
R. D. Lawson, M. H. Macfarlane: Nucl. Phys. 66, 80 (1965)
G. Racah: Phys. Rev. 76, 1352 (1949), Table I
L. Armstrong, B. R. Judd: Proc. R. Soc. London A 315, 27, 39 (1970)
B. R. Judd, S. Li: J. Phys. B 22, 2851 (1989)
B. R. Judd, G. M. S. Lister, M. A. Suskin: J. Phys. B 19, 1107 (1986)
B. R. Judd: Phys. Rep. 285, 1 (1997)
B. R. Judd, E. Lo: Phys. Rev. Lett. 85, 948 (2000)
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© 2006 Springer-Verlag
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Judd, B. (2006). Second Quantization. In: Drake, G. (eds) Springer Handbook of Atomic, Molecular, and Optical Physics. Springer Handbooks. Springer, New York, NY. https://doi.org/10.1007/978-0-387-26308-3_6
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DOI: https://doi.org/10.1007/978-0-387-26308-3_6
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