Maple procedures for the coupling of angular momenta. IX. Wigner D-functions and rotation matrices

Abstract The Wigner D-functions, D p q j ( α , β , γ ) , are known for their frequent use in quantum mechanics. Defined as the matrix elements of the rotation operator R ˆ ( α , β , γ ) in R 3 and parametrized in terms of the three Euler angles α, β, and γ, these functions arise not only in the transformation of tensor components under the rotation of the coordinates, but also as the eigenfunctions of the spherical top. In practice, however, the use of the Wigner D-functions is not always that simple,... Title of program: RACAH Catalogue Id: ADFV_v9_0 Nature of problem The Wigner D-functions and (reduced) rotation matrices occur very frequently in physical applications. They are known not only as the (infinite) representation of the rotation group but also to obey a number of integral and summation rules, including those for their orthogonality and completeness. Instead of the direct computation of these matrices, therefore, one first often wishes to find algebraic simplifications before the computations can be carried out in practice. 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)