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The term R-matrix has several meanings, depending on the field of study.
The term R-matrix is used in connection with the Yang–Baxter equation, first introduced in the field of statistical mechanics in the works of J. B. McGuire in 1964[1] and C. N. Yang in 1967[2] and in the group algebra of the symmetric group in the work of A. A. Jucys in 1966.[3]
![{\displaystyle \mathbb {C} [S_{n}]}](http://wikimedia.org/api/rest_v1/media/math/render/svg/03192415c4c777069325cf912b2d2e8ef259d00b)
The classical R-matrix arises in the definition of the classical Yang–Baxter equation.[4]
In quasitriangular Hopf algebra, the R-matrix is a solution of the Yang–Baxter equation.
The numerical modeling of diffraction gratings in optical science can be performed using the R-matrix propagation algorithm.[5]
There is a method in computational quantum mechanics for studying scattering known as the R-matrix. This method was originally formulated for studying resonances in nuclear scattering by Wigner and Eisenbud.[6] Using that work as a basis, an R-matrix method was developed for electron, positron and photon scattering by atoms.[7] This approach was later adapted for electron, positron and photon scattering by molecules.[8][9][10]
R-matrix method is used in UKRmol[11] and UKRmol+[12] code suits. The user-friendly software Quantemol Electron Collisions (Quantemol-EC) and its predecessor Quantemol-N are based on UKRmol/UKRmol+ and employ MOLPRO package for electron configuration calculations.
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