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Chaotic Behavior in Quantum Systems pp 37–76Cite as

The Relation Between Quantum Mechanics And Classical Mechanics: A Survey Of Some Mathematical Aspects

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Part of the book series: NATO ASI Series ((NSSB,volume 120))

Abstract

We give a survey of some mathematical work on the relation between quantum mechanical quantities like eigenvalues and eigenfunctions of Schrödinger operators and classical mechanical quantities, like classical actions computed along classical paths and lengths of geodesies. In particular we discuss the distribution of eigenvalues for a domain Rd or a Riemannian manifold. We also single out the manifolds for which the heat kernel and the spectrum of the Laplacian are given entirely by (the lengths of) geodesies, i.e., by classical orbits.

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Authors and Affiliations

  1. Mathematisches Institut, Ruhr-Universität Bochum, 4630, Bochum 1, Fed. Rep. Germany

    Sergio Albeverio

  2. Centre de Physique Théorique, CNRS, Luminy, Case 907, F-13288, Marseille Cedex 9, France

    Teresa Arede

  3. Faculdade de Engenharia (DEMEC), Universidade do Porto, R. dos Bragas, 4000, Porto, Portugal

    Teresa Arede

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  1. Sergio Albeverio
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  1. Alessandro Volta Center for Scientific Culture, Como, Italy

    Giulio Casati

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Albeverio, S., Arede, T. (1985). The Relation Between Quantum Mechanics And Classical Mechanics: A Survey Of Some Mathematical Aspects. In: Casati, G. (eds) Chaotic Behavior in Quantum Systems. NATO ASI Series, vol 120. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2443-0_3

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