N-level quantum systems and Gegenbauer polynomials
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 polynomials of a discrete variable has been applied. Using classic and non-classic Gegenbauer orthogonal polynomials we find and analyse exact solutions for special case with N=5. Various initial conditions for the 5-level quantum systems have been considered.