# R-matrix

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. This is an equation which was first introduced in the field of statistical mechanics, taking its name from independent work of C. N. Yang and R. J. Baxter. The classical R-matrix[1] arises in the definition of the classical Yang–Baxter equation.

In quasitriangular Hopf algebra, where 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.[2]

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.[3] Using that work as a basis, an R-matrix method was developed for electron, positron and photon scattering by atoms.[4] This approach was later adapted for electron, positron and photon scattering by molecules.[5]

## References

1. ^ B.A. Kupperschmidt, Journal of Nonlinear Mathematical Physics 1999, Vol. 6, No. 4, p.448ff
2. ^ Lifeng Li, Bremmer series, R-matrix propagation algorithm, and numerical modeling of diffraction gratings, Journal of the Optical Society of America A, Vol. 11, Issue 11, pp. 2829–2836
3. ^ L. Eisenbud and E. P. Wigner. Phys. Rev. Vol. 72 (1947) p.29
4. ^ P.G. Burke, A. Hibbert and W.D. Robb, J. Phys. B: At. Mol. Phys. 4 (1971), p.153.
5. ^ C J Gillan, J Tennyson, and P G Burke, in Computational Methods for Electron-Molecule Collisions, eds. W M Huo and F A Gianturco, (Plenum, New York, 1995), p. 239