Differential equations of spin dynamics and asymptotic expansion of quantum mean values near the classical limit. III

Abstract

A study is made of the asymptotic behavior of the functional analogs of the coefficients of vector addition (Clebsch-Gordan coefficients) introduced by means of atomic coherent states for large values of the angular momenta. The cases J₁ J₂, J₃ ≫ 1 and J₁, J₃ ≫ J₂, where J₁ and J₂ are the original angular momenta and J₃ is the resultant, are investigated. It is shown that the investigated functions are transformed for large J into narrow distributions, which makes it possible to expand integrals containing such functions in asymptotic series in powers of J⁻¹. The quantum rule for adding angular momenta, formulated in functional language, goes over into the classical one in the limit J → ∞ The possibility of using these relations to describe molecules with rotational degrees of freedom is discussed.