Near/far-side angular decompositions of Legendre polynomials using the amplitude-phase method
 作者： Karl-Erik Thylwe,  Patrick McCabe 作者单位： 1Royal Institute of Technology2CCDC 刊名： Journal of Mathematical Chemistry, 2017, Vol.55 (8), pp.1638-1648 来源数据库： Springer Nature Journal DOI： 10.1007/s10910-017-0752-x 关键词： Scattering;  Legendre polynomials;  Amplitude-phase method;  Differential cross section;  Chemical reaction theory; 英文摘要： A decomposition of Legendre polynomials into propagating angular waves is derived with the aid of an amplitude-phase method. This decomposition is compared with the ’Nussenzveig/Fuller’ so called near/far-side decomposition of Legendre polynomials. The latter decomposition requires the Legendre function of the second kind. This is not the case with the amplitude-phase decomposition. Both representations have the same asymptotic expressions for large values of $$(l+1/2)\sin \theta$$ , where l and $$\theta$$ are the polynomial degree and the angle respectively. Furthermore, both components of both representations satisfy the Legendre differential equation. However, we show the two representations are not identical. 原始语种摘要： A decomposition of Legendre polynomials into propagating angular waves is derived with the aid of an amplitude-phase method. This decomposition is compared with the ’Nussenzveig/Fuller’ so called near/far-side decomposition of Legendre polynomials. The latter decomposition requires the Legendre function of the second kind. This is not the case with the amplitude-phase decomposition. Both representations have the same asymptotic expressions for large values of $$(l+1/2)\sin \theta$$ , where l and $$\theta$$ are the polynomial degree and the angle respectively. Furthermore, both components of both representations satisfy the Legendre differential equation. However, we show the two representations are not identical.

• decomposition　分解
• method　方法
• asymptotic　渐近的
• polynomial　多项式
• phase　相位
• amplitude　振幅
• theta　希腊字母θ
• reaction　反酌
• theory　理论
• satisfy　满足