The role of discrete orthogonal polynomials in constructing solutions of the dynamical equations describing coherent excitation of quantum systems in the field of laser radiation

Abstract

The paper presents and implements an algorithm for constructing exact analytical solutions of the corresponding differential equations. The solutions are obtained without integration of the equations but with the use of methods of a discrete mathematics. The discrete Fourier transform of the equations and discrete orthogonal polynomials in Fourier space are used. Specially constructed polynomials are used and the solutions of the coherent dynamics equations of some quantum systems excited by laser radiation are given.