Maple procedures for the coupling of angular momenta. IV. Spherical harmonics

Abstract Spherical harmonics play a crucial role in theoretical physics since they represent a complete and orthonormal set of functions on the unit sphere. The spherical harmonics are therefore applied in many different fields of physics including classical field theory as well as the treatment of quantum many-particle systems. Along with their well-known properties, they are frequently utilized to evaluate one- and many-particle matrix elements from atomic and nuclear structure theory analytically. ... Title of program: RACAH Catalogue Id: ADFV_v4_0 [ADOR] Nature of problem Spherical harmonics are applied in many fields of physics. In classical electrodynamics, for instance, the spherical harmonics may be utilized to expand the electro-magnetic field of a charge distribution in terms of its multipoles. The spherical harmonics also provide an important basis in quantum mechanics for classifying one- and many-particle states since they are simultaneous eigenfunctions of one component and of the square of the orbital angular momentum operator -ir x Delta. In many-part ... Versions of this program held in the CPC repository in Mendeley Data ADFV_v1_0; Racah; 10.1016/S0010-4655(97)00032-5 ADFV_v2_0; Racah; 10.1016/S0010-4655(98)00021-6 ADFV_v3_0; RACAH; 10.1016/S0010-4655(00)00234-4 ADFV_v4_0; RACAH; 10.1016/S0010-4655(01)00218-1 ADFV_v5_0; RACAH; 10.1016/S0010-4655(01)00219-3 ADFV_v6_0; RACAH; 10.1016/S0010-4655(02)00591-X ADFV_v7_0; RACAH; 10.1016/S0010-4655(03)00227-3 ADFV_v8_0; RACAH; 10.1016/j.cpc.2004.11.003 ADFV_v9_0; RACAH; 10.1016/j.cpc.2005.12.008 ADFV_v10_0; RACAH; 10.1016/j.cpc.2009.06.018 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

**摘要**：球谐函数（Spherical harmonics）在理论物理中占据核心地位，因其构成了单位球面上一组完备且正交归一的函数集合。故而球谐函数被广泛应用于物理学诸多分支，涵盖经典场论与量子多体系统的研究。凭借其广为人知的优良性质，球谐函数常被用于从原子与原子核结构理论中解析计算单粒子及多粒子矩阵元……

程序名称：RACAH
目录ID：ADFV_v4_0 [ADOR]
问题本质：球谐函数在物理学众多领域均有应用。例如在经典电动力学中，可借助球谐函数将电荷分布的电磁场按多极矩展开。在量子力学领域，球谐函数亦是分类单粒子与多粒子态的重要基矢，因其同时是轨道角动量算符的单个分量以及轨道角动量平方算符的本征函数。在多体……

本程序在Mendeley Data的《计算机物理学报》（Computer Physics Communications，简称CPC）库中的版本信息如下：
ADFV_v1_0; Racah; 10.1016/S0010-4655(97)00032-5
ADFV_v2_0; Racah; 10.1016/S0010-4655(98)00021-6
ADFV_v3_0; RACAH; 10.1016/S0010-4655(00)00234-4
ADFV_v4_0; RACAH; 10.1016/S0010-4655(01)00218-1
ADFV_v5_0; RACAH; 10.1016/S0010-4655(01)00219-3
ADFV_v6_0; RACAH; 10.1016/S0010-4655(02)00591-X
ADFV_v7_0; RACAH; 10.1016/S0010-4655(03)00227-3
ADFV_v8_0; RACAH; 10.1016/j.cpc.2004.11.003
ADFV_v9_0; RACAH; 10.1016/j.cpc.2005.12.008
ADFV_v10_0; RACAH; 10.1016/j.cpc.2009.06.018

本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2018）。