Two-photon processes based on quantum commutators

TL;DR

This paper introduces a novel quantum mechanical method for calculating two-photon processes using a commutator-based perturbation expansion, simplifying the analysis of scattering phenomena like Rayleigh and Raman scattering.

Contribution

The paper presents a new approach that replaces infinite sums with a commutator series, enabling closed-form solutions and convergence analysis for complex two-photon processes.

Findings

Distinguishes classical and quantum scattering contributions.

Provides closed-form solutions for certain cases.

Offers a convergent method for complex scenarios.

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.