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）在理论物理学中具有至关重要的地位，因其为单位球面上一组完备且正交归一的函数集合。因此，球谐函数被广泛应用于物理学的诸多分支领域，涵盖经典场论与量子多粒子系统的研究。凭借其广为人知的优良性质，球谐函数常被用于解析计算原子与原子核结构理论中的单粒子及多粒子矩阵元。 …… 程序名称：RACAH 目录编号：ADFV_v4_0 [ADOR] 待解决问题 球谐函数在物理学诸多领域均有应用。例如在经典电动力学中，可利用球谐函数将电荷分布的电磁场按多极矩展开。此外，球谐函数同时是轨道角动量算符$-ioldsymbol{r} imes abla$的一个分量与轨道角动量平方算符的共同本征函数，因此在量子力学中，它也是分类单粒子与多粒子态的重要基础。在多粒子…… Mendeley数据集中CPC仓库内的本程序各版本 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托管的CPC程序库（1969-2018）