球坐标D函数D_(m′m)~j(θ,φ,ω)与D_(m′m)~j的傅里叶级数表示

The Fourier series representation of spherical coordinate D function D_(m′m)~j(θ,φ,ω) and D_(m′m)~j(ω)

推出了转动元球坐标参数与欧拉角参数之间的相互变换公式;引入了用球坐标参数表示的D 函数Djm′m(θ,φ,ω) 并讨论了它的一些重要性质,由此还得到了djm′m( ω) 的傅里叶级数表示,表明函数矩阵dj( ω) 完全由它在ω= π2 时的取值矩阵dj π2 决定,而后者的计算又可归结为求一个简单的整数矩阵Cj.

A concise and elegant formula of mutual transformation between the two different parametrizations of 3-dim.rotation group SO(3) is derived,a new D function D j m′m (θ,φ,ω) using spherical coordinates (θ,φ,ω) as parametens is introduced and through its analysis the Fourier series representation of d j m′m (ω) is discovered,which shows that the matrix of d function d j(ω) is completely determined by its value at point ω=π2 d jπ2,whose calculation is reduced to computing a simple matrix of integers C j.