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Abstract
The localization behavior of one-dimensional quantum systems for ℏ→0 is investigated by semiclassical methods. In particular the localization of the quantum probability around turning points of arbitrary even order associated to classical hyperbolic orbits is considered and a relation of the localization speed in ℏ with the classical motion is established. Our analysis is based on local norm comparisons of solutions to Schrödinger type equations; it relies mainly on a combination of scaling and asymptotic arguments and thus evades the use of special functions. Applications of the results to separable multidimensional Schrödinger equations are indicated by a brief discussion of the one-electron diatomic molecular ion.
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