Analytic method in dynamics of quantum multilevel
systems – models
of multiphoton excitation of molecules
by infrared laser radiation
Savva V.A., Zelenkov V.I., Mazurenko A.S., Dolya Z.E.
An analytic method to obtain exact solutions for equations which describe coherent dynamics of multilevel quantum systems is presented. The method is based on using an integral transform and orthogonal polynomials. A correspondence of a multilevel quantum system with specific conditions of excitation to every orthogonal polynomials system was established. The known orthogonal polynomials and special constructed new polynomials to find corresponding to them multilevel quantum systems (system characteristics found, conditions of their excitation defined) are used. Exact analytic solutions which describe dynamics of the systems in radiation field are obtained. The mentioned correspondence: orthogonal polynomials – quantum systems leads to natural classification of multilevel quantum systems with exact solution which is obtained with aid of the mentioned method. Paths of generalizing of the method to increase quantity of multilevel systems with solution in an analytical form and to apply it for an analysis of coherent and non-coherent dynamics of multilevel systems are delineated.