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.

Nonlinear response properties of atomic hydrogen under quantum plasma environment: A time‐dependent variation perturbation study on hyperpolarizability and two‐photon excitations

“…The ground-state wave function in plasma environment is expanded in terms of four-parameter Slater basis sets of fixed exponents represented by Equation 5, and the linear variation parameters are determined from solutions of generalized eigenvalue Equation (6). Variational principle is adopted to construct the perturbed wave functions up to second order, all of which are expanded in eight-parameter Slater basis sets following Equations (26) and (27). For free H atom, a one-parameter analytic wave function for the ground state is sufficient.…”

“…Subsequently, it was investigated widely by different authors due to its experimental feasibility and applications in NLO properties and is still an active area of research. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] For one-electron systems without confinement, solutions of a nonrelativistic Schrödinger equation in an external electric field yield exact values of polarizabilities and hyperpolarizabilities, [27][28][29][30] and departure from the "pure" Coulomb potential demands alternative theoretical approaches. It is well known that pole positions of frequency-dependent linear polarizability α(ω) furnish accurate representations of single-photon excited states.…”