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[Help-gsl] Wigner d-matrix

From: Jesse Johnson
Subject: [Help-gsl] Wigner d-matrix
Date: Wed, 11 Nov 2015 16:19:17 -0500
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101 Thunderbird/38.3.0

Hello all,

While it seems most of contribs/wigner.h was ported to specfunc/gsl_sf_coupling.h, the Wigner (small) d-matrix was not. Indeed, the wigner_drot function seems to be the only reason for keeping the contribs file around. Is there a particular reason this function has not been ported? If not, what would porting it entail?

I assume the main obstacle is adding tests and verifying the implementation. As-is, simply copy/pasting the files into specfunc/, renaming them according to gsl convention, and adding the necessary lines to specfunc/ allows me to compile wigner.h into the library as-is.

I manually tested the function via a wrapper I wrote in Julia and was able to reproduce the expected results for j = 1/2, 1, 3/2, and 2 (i.e. j = int 1, 2, 3, 4 according to the parameter convention of multiplying by two to get an integer). All results were as expected based on the analytic formula on Wikipedia:

For example, for j = m' = m = 3/2 (i.e., int 3) and theta = 3/4 * pi:

julia> theta = 3/4 * pi
julia> (1 + cos(theta)) / 2 * cos(theta/2)
julia> sf_wigner_drot(3, 3, 3, theta)

It seems strange to have the Wigner coefficients but not the rotation matrix, and I am sure others would find it useful, so please consider allowing this addition.

Thank you,

Jesse Johnson

Ph.D. candidate
Institute for Quantitative Biomedicine @ Rutgers University (address@hidden)

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