Applying \textit{Mathematica} to the analytical solution of the nonlinear Heisenberg operator equations (Q1299700)

This paper is concerned with the series solution of nonlinear Heisenberg operator equations which arise in some fields of quantum physics, e.g. in some models that describe the quantum properties of radiation obtained in the process of three-wave interaction. The author considers processes described by a set of ordinary differential equations with annihilation and creation operators like those which appear in nonlinear optical waves. In this frame he shows that the evolution of some standard operators can be described by using instructions of \textit{Mathematica}. In addition some statistical quantities such as the variance, the mean value and correlation coefficient of two operators can be given by means of \textit{Mathematica} instructions. Finally the author applies this approach to solve the problem of second harmonic generation by mixing orthogonally polarized fundamental waves in a quadratic \(\chi^{(2)}\) nonlinear medium.