Quantum similarity measures expectation functions

Second, the calculated (as well as the measured) distributions are remarkably smooth although often more than fifty or so rotational states are populated. If so many quantum states take part in a collision, one intuitively expects pronounced interference oscillations. The reason for the absence of interferences is the uniqueness between 70 and j one and only one trajectory contributes to the cross section for a specific final rotational state. If two trajectories that lead to the same j had comparable weights, the constructive and destructive interference, within a semiclassical picture, would lead to pronounced oscillations (Miller 1974, 1975 Korsch and Schinke 1980 Schinke and Bowman 1983). These so-called supernumerary rotational rainbows are well established in full collisions (Gottwald, Bergmann, and Schinke 1987). If the weighting function W (70) is sufficiently wide that both trajectories contribute to the dissociation cross section, similar oscillations may also exist in photodissociation (see, for example, Philippoz, Monot, and van den Bergh 1990 and Miller, Kable, Houston, and Burak 1992). 

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