N-level quantum systems and Legendre functions
Mazurenko A.S., Savva V.A.
An excitation dynamics of new equidistant N-level quantum systems in monochromatic field has been investigated. To obtain exact analytical solutions of dynamics equations an analytic method based on orthogonal functions of real argument has been proposed. Using orthogonal Legendre functions we have found exact analytical expression for probability amplitude of population of level n. Various initial conditions for excitation of the N-level quantum systems have been considered.