Geodesic
Quasiclassical asymptotic behavior for Wigner's $3j$-symbols
Teoretičeskaâ i matematičeskaâ fizika, Tome 34 (1978) no. 1, pp. 110-121 
K. S. Borodin; A. E. Kroshilin; V. V. Tolmachev. Quasiclassical asymptotic behavior for Wigner's $3j$-symbols. Teoretičeskaâ i matematičeskaâ fizika, Tome 34 (1978) no. 1, pp. 110-121. http://geodesic.mathdoc.fr/item/TMF_1978_34_1_a9/
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     title = {Quasiclassical asymptotic behavior for {Wigner's} $3j$-symbols},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1978_34_1_a9/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Expressions for Wigner's $3j$-symbols are considered which hold in the asymptotic limit of large quantum numbers of the angular momenta. It is shown that, depending on the quantum numbers of the angular momentum projections, there exist three types of expression: “classical”, “tunnel”, “transition”. Numerical calculations have been made of the values of definite $3j$-symbols in accordance with exact and approximate expressions, and these show that the expressions have a good accuracy already for angular momenta of order 5.

[1] E. Vigner, Teoriya grupp i ee prilozheniya k kvantovomekhanicheskoi teorii atomnykh spektrov, gl. 24, 27, IL, 1961 | MR

[2] Spectroscopic and group theoretical methods in physics, Racah Memorial Volume, Amsterdam, 1968

[3] P. T. Brassard, H. A. Tolholk, Physica, 23 (1957), 955 | DOI | MR

[4] A. K. Edmonds, Angular Momentum in Quantum Mechanics, Geneva, 1955 | MR

[5] N. Ya. Vilenkin, Spetsialnye funktsii i teoriya predstavlenii grupp, «Nauka», 1965 | MR

[6] A. E. Kroshilin, V. V. Tolmachev, Usp. matem. n., 29:6 (1974), 201–202 | MR

[7] A. E. Kroshilin, V. V. Tolmachev, Issledovaniya po mekhanike zhidkostei i tverdykh tel, Sb., MGU, 1977, 10

[8] K. Schulten, R. G. Garden, J. Math. Phys., 16 (1975), 1971 | DOI | MR

[9] E. T. Kopson, Asimptoticheskie razlozheniya, «Mir», 1966

[10] Dzh. Kheding, Vvedenie v metod fazovykh integralov, «Mir», 1965

[11] E. Kondon, G. Shortli, Teoriya atomnykh spektrov, IL, 1949

[12] L. Mishel, M. Shaaf, Simmetriya v kvantovoi fizike, «Mir», 1974