Solving method without integration of some differential equation systems for coherent dynamics of quantum media excited by laser radiation

Abstract

A pragmatic mechanism to obtain exact analytical solutions of equations describing the coherent dynamics of quantum multilevel systems by laser radiation is implemented. The technique shows interesting features and significant connections between different mathematical structures for constructing exact solutions for a large family of quantum systems, and is based on discrete orthogonal polynomials which are used to express the Fourier spectra of the probability amplitudes of an excited quantum system.

Subject Classification:

• Primary 93A30
• Secondary 49K15

Keywords:

• Dynamical systems in quantum mechanics
• Exact solutions
• Discrete orthogonal polynomials
• Discrete Fourier transform