article published yes Filippo Fratini author Laleh Safari author 3C325E5E-F248-11E8-B48F-1D18A9856A87 Pedro Amaro author José Santos author MiLe department International IST Postdoc Fellowship Programme project 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. American Physical Society2018 eng 1801.06892 00043029680000810.1103/PhysRevA.97.043842 974 Fratini, Filippo, et al. “Two-Photon Processes Based on Quantum Commutators.” <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>, vol. 97, no. 4, American Physical Society, 2018, doi:<a href="https://doi.org/10.1103/PhysRevA.97.043842">10.1103/PhysRevA.97.043842</a>. Fratini F, Safari L, Amaro P, Santos J. Two-photon processes based on quantum commutators. <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>. 2018;97(4). doi:<a href="https://doi.org/10.1103/PhysRevA.97.043842">10.1103/PhysRevA.97.043842</a> Fratini, Filippo, Laleh Safari, Pedro Amaro, and José Santos. “Two-Photon Processes Based on Quantum Commutators.” <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>. American Physical Society, 2018. <a href="https://doi.org/10.1103/PhysRevA.97.043842">https://doi.org/10.1103/PhysRevA.97.043842</a>. F. Fratini, L. Safari, P. Amaro, J. Santos, Physical Review A - Atomic, Molecular, and Optical Physics 97 (2018). Fratini F, Safari L, Amaro P, Santos J. 2018. Two-photon processes based on quantum commutators. Physical Review A - Atomic, Molecular, and Optical Physics. 97(4). Fratini, F., Safari, L., Amaro, P., &#38; Santos, J. (2018). Two-photon processes based on quantum commutators. <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevA.97.043842">https://doi.org/10.1103/PhysRevA.97.043842</a> F. Fratini, L. Safari, P. Amaro, and J. Santos, “Two-photon processes based on quantum commutators,” <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>, vol. 97, no. 4. American Physical Society, 2018. 2942018-12-11T11:45:40Z2025-04-15T06:50:21Z