Two-photon processes based on quantum commutators

F. Fratini, L. Safari, P. Amaro, J. P. Santos

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
9 Downloads (Pure)


We developed a 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 lets us derive general results concerning light scattering. Finally, possible extensions to the developed formalism are discussed.

Original languageEnglish
Article number043842
JournalPhysical Review A
Issue number4
Publication statusPublished - 18 Apr 2018


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