Maple procedures for the coupling of angular momenta. VI. LS–jj transformations

Maple Procedures for the Coupling of Angular Momenta. Vi. Ls − Jj Transformations Program Summary Long Write–up

Transformation matrices between different coupling schemes are required, if a reliable classification of the level structure is to be obtained for open–shell atoms and ions. While, for instance, relativistic computations are traditionally carried out in jj−coupling, a LSJ coupling notation often occurs much more appropriate for classifying the valence–shell structure of atoms. Apart from the (k...

Maple procedures for the coupling of angular momenta. An up-date of the Racah module

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

The Wigner D-functions, D pq(α,β, γ ), are known for their frequent use in quantum mechanics. Defined as the matrix elements of the rotation operator R̂(α,β, γ ) in R3 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...

Notes 17 : Coupling of Angular Momenta 3

In these notes we discuss the coupling or addition of angular momenta, a problem that arises whenever different subsets of the degrees of freedom of a system, each possessing its own angular momentum operator, are combined to form the whole system. In such cases, the whole system also possesses an angular momentum operator. Alternatively, we may say that there is an action of the rotations on e...

Coupling of Ket Spaces and the Addition of Angular Momenta

In these notes we discuss the coupling of ket spaces of systems to form the ket spaces of larger systems. The constituent systems may be independent of each other in some physical circumstances or in some models, while in other circumstances or more realistic models they may become coupled. We will see many examples of this process in this course, including the coupling of spin and orbital degr...