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arXiv · 1801.06892

Two-photon processes based on quantum commutators

Filippo Fratini·Laleh Safari·Pedro Amaro·José-Paulo Santos
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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.

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Filippo Fratini, Laleh Safari, Pedro Amaro, José-Paulo Santos. 2018-01-21. Two-photon processes based on quantum commutators. https://doi.org/10.1103/physreva.97.043842

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