“Wigner 3j-Symbol”的概念、定义、习题解题方法及翻译-数学辞典

单词

Wigner 3j-Symbol

释义

Wigner 3j-Symbol

The Wigner symbols are written

(1)

and are sometimes expressed using the related Clebsch-Gordan Coefficients

(2)

(Condon and Shortley 1951, pp. 74-75; Wigner 1959, p. 206), or Racah V-Coefficient

(3)

Connections among the three are

(4)

(5)

(6)

The Wigner

-symbols have the symmetries





			(7)

The symbols obey the orthogonality relations

(8)

(9)

where

is the Kronecker Delta.

General formulas are very complicated, but some specific cases are


	(10)


	(11)

(12)

for

For Spherical Harmonics ,


	(13)

For values of

obeying the Triangle Condition


	(14)

and

(15)

See also Clebsch-Gordan Coefficient, Racah V-Coefficient, Racah W-Coefficient, Wigner 6j-Symbol, Wigner 9j-Symbol

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Vector-Addition Coefficients.'' §27.9 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 1006-1010, 1972.

Condon, E. U. and Shortley, G. The Theory of Atomic Spectra. Cambridge, England: Cambridge University Press, 1951.

de Shalit, A. and Talmi, I. Nuclear Shell Theory. New York: Academic Press, 1963.

Gordy, W. and Cook, R. L. Microwave Molecular Spectra, 3rd ed. New York: Wiley, pp. 804-811, 1984.

Messiah, A. ``Clebsch-Gordan (C.-G.) Coefficients and `' Symbols.'' Appendix C.I in Quantum Mechanics, Vol. 2. Amsterdam, Netherlands: North-Holland, pp. 1054-1060, 1962.

Rotenberg, M.; Bivens, R.; Metropolis, N.; and Wooten, J. K. The and Symbols. Cambridge, MA: MIT Press, 1959.

Shore, B. W. and Menzel, D. H. Principles of Atomic Spectra. New York: Wiley, pp. 275-276, 1968.

Sobel'man, I. I. ``Angular Momenta.'' Ch. 4 in Atomic Spectra and Radiative Transitions, 2nd ed. Berlin: Springer-Verlag, 1992.

Wigner, E. P. Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, expanded and improved ed. New York: Academic Press, 1959.

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