Abstract
Universal behavior of Gaussian-Klauder states emerges near soft classical turning points, as expressed through a complex-valued Airy transformation that approximates the wave function. Study of these classical turning points provides analytic evidence that Gaussian-Klauder states generally display recurrent localization for many classical orbital periods. Analytic position and momentum moments of the wave function are determined from this approximation, leading in part to connections with the traditionally chosen positional Gaussian wave functions as the limit of large energy uncertainty. Application of this procedure to hydrogenic states of maximal eccentricity leads to the classical limit of recurrent collisional bouncing in the Kepler problem, via the explicit construction of states that maintain phase space localization for many orbital periods.
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