Two-photon processes based on quantum commutators
Abstract
We developed a new method to calculate two-photon processes in quantum mechanics that replaces the infinite summation over the intermediate states by a perturbation expansion. This latter consists of a series of commutators that involve position, momentum and hamiltonian quantum operators. We analyzed several single- and many-particle cases for which a closed form solution to the perturbation expansion exists, as well as more complicated cases for which a solution is found by convergence. Throughout the article, Rayleigh and Raman scattering are taken as examples of two-photon processes. The present method provides a clear distinction between the Thomson scattering, regarded as classical scattering, and quantum contributions. Such a distinction let us derive general results concerning light scattering. Finally, possible extensions to the developed formalism are discussed.
Cite
@article{arxiv.1801.06892,
title = {Two-photon processes based on quantum commutators},
author = {Filippo Fratini and Laleh Safari and Pedro Amaro and José-Paulo Santos},
journal= {arXiv preprint arXiv:1801.06892},
year = {2018}
}