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

Evaluation of the rotation matrices in the basis of real spherical harmonics

Rotation matrices (or Wigner D functions) are the matrix representations of the rotation operators in the basis of spherical harmonics. They are the key entities in the generation of symmetry-adapted functions by means of projection operators. Although their expression in terms of ordinary (complex) spherical harmonics and Euler rotation angles is well known, an alternative representation using...

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

ar X iv : c on d - m at / 0 10 51 37 v 2 8 M ay 2 00 1 Wigner quasi - distribution function for charged particles in classical electromagnetic fields

A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relation to the axial gauge is discussed, as well as the relation between the kinetic and canonical momenta in the Wigner representation. Gauge-invariant quantum analogs of Hamilton-Jacobi and Boltzmann kinetic equations are formulated for arbitrary cl...

Analytical Scheme Calculations of Angular Momentum Coupling and Recoupling Coefficients

We investigate the Scheme programming language opportunities to analytically calculate the ClebschÄGordan coefˇcients, Wigner 6j and 9j symbols, and general recoupling coefˇcients that are used in the quantum theory of angular momentum. The considered coefˇcients are calculated by a direct evaluation of the sum formulas. The calculation results for large values of quantum angular momenta were c...