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.
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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
球谐函数在理论物理学中扮演着至关重要的角色，因其能够表征单位球面上的完备正交函数集。因此，球谐函数被广泛应用于物理学的众多领域，包括经典场论以及量子多粒子系统的处理。除了其众所周知的性质外，球谐函数还常被用来从原子和核结构理论中解析地计算一粒子及多粒子的矩阵元...

程序名称：RACAH
目录编号：ADFV_v4_0 [ADOR]

问题性质
球谐函数在物理学诸多领域得到应用。例如，在经典电动力学中，球谐函数可用于将电荷分布的电场展开为其多极矩的形式。在量子力学中，球谐函数亦构成一个重要的基，用于对单粒子或多粒子状态进行分类，因为它们是轨道角动量算符的某个分量及其平方的共轭特征函数...

该程序版本存放在Mendeley数据中的CPC程序库
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

此程序已从贝尔法斯特女王大学（1969-2018年）所持有的CPC程序库中导入。