The elaboration of analytic methods for investigation of the dynamics of multilevel quantum systems
Mazurenko A.S., Savva V.A.
The new modification of the analytic method for solving of multilevel dynamics equations modeling, in particular, processes of multiphoton excitation of molecules by powerful IR laser radiation, has been elaborated. The method is based on construction of new orthogonal polynomial sequences and application of them to investigate dynamics of multilevel systems excitation. With the using Christoffel formula new families of the Christoffel-Legendre orthogonal polynomials of the first, second, and fourth degrees have been constructed, they have been applied to describe both equidistant multilevel quantum systems and non-equidistant ones. With the aid of generalization of Christoffel formula, i.e. Christoffel-Uvarov formula, new families of the Uvarov-Legendre orthogonal polynomials of the first, second, and fourth degrees have been defined to obtain solutions modeling lock effects of molecular excitation. The connection of characteristics of multilevel systems, corresponding to polynomials with the mutual inverse weights, has been revealed and investigated.