Wigner.m

Wigner D matrices, defined as (Brink & Satchler, Eq 2.13):

      D=expm(-1i*Lz*alp)*expm(-1i*Ly*bet)*expm(-1i*Lz*gam);

where Lx, Ly, Lz are Cartesian spin operators.

Syntax

    D=wigner(l,alp,bet,gam)

Parameters

      l    - rank of the Wigner matrix, may be half-integer

    alp    - alpha Euler angle, radians

    bet    - beta Euler angle, radians

    gam    - gamma Euler angle, radians

Outputs

      D    - Wigner D matrix with rows and columns sorted
             by descending ranks, for example (l=2):

                     [D( 2,2)  ...  D( 2,-2)
                        ...    ...    ...  
                      D(-2,2)  ...  D(-2,-2)]

Notes

ZYZ convention is used for Euler angles, see Brink and Satchler, Figures 1 and 2. See the rotation conventions page for a detailed description of the rotation convention used consistently everywhere in Spinach.

The output is to be used as y=D*x, where x is a column vector of irreducible spherical tensor coefficients, listed vertically in the order: T(2,2), T(2,1), T(2,0), T(2,-1), T(2,-2).

See also

add_spins.m, anax2dcm.m, anax2quat.m, axis_tsymm.m, cg_fast.m, clebsch_gordan.m, comm.m, dcm2euler.m, dcm2wigner.m, euler2dcm.m, euler_sup.m, hilb2liouv.m, irr_sph_ten.m, ist_product_table.m, lorentz.m, mat2sphten.m, multipack.m, pauli.m, perm_group.m, quat2anax.m, rocomm.m, rotmat_align.m, rotor_stack.m, rwalk.m, sle_operators.m, sorensen.m, spher_harmon.m, sphten2mat.m, stev2sph.m, stevens.m, superop.m, twospinist.m, wigner_3j.m, wigner_6j.m, xyz2sph.m, Kernel_utilities

Version 2.8, authors: Ilya Kuprov