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 In physics, the Yang–Baxter equation (or star–triangle relation) is a consistency equation which was first introduced in the field of statistical mechanics. It depends on the idea that in some scattering situations, particles may preserve the ...

. 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 arises in the definition of the classical Yang–Baxter equation. In

quasitriangular Hopf algebra In mathematics, a Hopf algebra, ''H'', is quasitriangularMontgomery & Schneider (2002), p. 72 if there exists an invertible element, ''R'', of H \otimes H such that :*R \ \Delta(x)R^ = (T \circ \Delta)(x) for all x \in H, where \Delta is the copr ...

, the R-matrix is a solution of the

. The numerical modeling of diffraction gratings in

optical science Atomic, molecular, and optical physics (AMO) is the study of matter-matter and light-matter interactions; at the scale of one or a few atoms and energy scales around several electron volts. The three areas are closely interrelated. AMO theory in ...

can be performed using the R-matrix propagation algorithm.

R-matrix method in quantum mechanics

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 Eugene Paul "E. P." Wigner ( hu, Wigner Jenő Pál, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his con ...

and Eisenbud. Using that work as a basis, an R-matrix method was developed for electron, positron and photon scattering by atoms. This approach was later adapted for electron, positron and photon scattering by molecules. R-matrix method is used in UKRmol and UKRmol+ code suits. The user-friendly software Quantemol Electron Collisions (Quantemol-EC) and its predecessor Quantemol-N are based on UKRmol/UKRmol+ and employ

MOLPRO MOLPRO is a software package used for accurate ''ab initio'' quantum chemistry calculations. It is developed by Peter Knowles at Cardiff University and Hans-Joachim Werner at Universität Stuttgart in collaboration with other authors. The emphasi ...

package for electron configuration calculations.

References

{{Reflist, 3 Matrices

R-matrix method in quantum mechanics

See also

References