Wave-packet dynamics and quantum beats

Quantum beats provide a useful tool in spectroscopy for the evaluation of fixed energy level differences. However, in wave-packet dynamics the motion of wave packets about molecular energy surfaces provides time-dependent energy differences. Thus a superposition of wave packets on two excited energy states can yield quantum beats with a time-dependent frequency that depends on the molecular dynamics. We explore this problem with examples and simple models of wave-packet quantum beats. The effects of separating wave packets, and wave packet dispersion, an of especial interest. Calculations are performed using a numerical integration of the time-dependent Schrodinger equation with three energy states and time-dependent couplings. The effects of spontaneous emission are determined by using a fully quantum mechanical Monte Carlo wave-function method.