Near/far-side angular decompositions of Legendre polynomials using the amplitude-phase method
作者: Karl-Erik ThylwePatrick McCabe
作者单位: 1Royal Institute of Technology
2CCDC
刊名: Journal of Mathematical Chemistry, 2017, Vol.55 (8), pp.1638-1648
来源数据库: Springer Journal
DOI: 10.1007/s10910-017-0752-x
关键词: ScatteringLegendre polynomialsAmplitude-phase methodDifferential cross sectionChemical 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.
全文获取路径: Springer  (合作)
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影响因子:1.226 (2012)

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关键词翻译
关键词翻译
  • 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