TITLE

On the semiclassical localization of the quantum probability

AUTHOR(S)

Duclos, P.; Hogreve, H.

PUB. DATE

May 1993

SOURCE

Journal of Mathematical Physics;May93, Vol. 34 Issue 5, p1681

SOURCE TYPE

Academic Journal

DOC. TYPE

Article

ABSTRACT

The localization behavior of one-dimensional quantum systems for h?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 h with the classical motion is established. Our analysis is based on local norm comparisons of solutions to Schr�dinger 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 Schr�dinger equations are indicated by a brief discussion of the one-electron diatomic molecular ion.

ACCESSION #

9824735

Tags: LOCALIZATION theory;  QUANTUM theory

 

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