A collinear model system

Kulander and Light (1980). The vertical lines indicate the energies of the symmetric stretch mode on top of the saddle of the upper electronic state and vss denotes the corresponding quantum number, (b) and (c) Absorption spectra for equilibrium bond distances which axe slightly longer respectively shorter than those with which the spectrum in (a) has been calculated. The dynamics in the upper state, however, is unaffected by this shift. Reproduced from Schinke and Engel (1990). 

The sinusoidal factor follows from the translation property of the Fourier transformation (Butkov 1968 ch.4). Thus, each spectrum di E) is a Gaussian in energy centered at E = /% and modulated by a sinusoidal function with wavelength 

The analysis presented so far explains the energy dependence of the spectrum in terms of the recurrences of the wavepacket. It does not, however, elucidate what kind of molecular motion actually causes the recurrences. In this particular example, the evolving wavepacket by itself does not clearly reveal the origin of the recurrences. The major part of the wavepacket follows the shortest route to dissociation and buries the much smaller portion, which returns at least once to the starting position. 

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