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Multiplicative formulation of quantum mechanics: A new setting for semi- classical analysis. (English) Zbl 0832.35120

Boutet de Monvel, Louis (ed.), Analyse algébrique des perturbations singulières. II. Méthodes différentielles. Conférences du symposium franco-japonais sur l’analyse algébrique des perturbations singulières, CIRM, Marseille-Luminy, France, October 20-26, 1991. Paris: Hermann. Trav. Cours. 48, 1-17 (1994).
Summary: A general semi-classical description, for the eigenfunctions of the multidimensional Schrödinger operator, cannot be based on the WKB method which is incompatible with classically ergodic behavior. An alternative, more general multiplicative parametrization of quantum wave functions is suggested, whereby the semi-classical behavior of eigenfunctions can be traced in the presence of classical ergodicity, in the form of diffusive patterns of phase-space zeros in the quantum wave functions.
For the entire collection see [Zbl 0824.00034].

MSC:

35Q40 PDEs in connection with quantum mechanics
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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