Dynamics of multilevel systems and orthogonal polynomials
Savva V.A., Zelenkov V.I., Mazurenko A.S.
The method to obtain exact analytical solutions of multilevel systems dynamics equations using orthogonal polynomials is set out. Three examples to use the method are given. The new solutions describe coherent excitation by quasiresonant infrared laser radiation of multilevel molecular systems with miscellaneous dependencies of radiation transition dipole moment on energy. Using of the polynomials to describe non-coherent dynamics of multilevel systems (vibrational relaxation of gas molecules in thermostatics capacity). A convenient form of the recurrent relation for orthogonal polynomials is introduced.