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

  • Sergio Albeverio
  • Teresa Arede
Part of the NATO ASI Series book 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.

Keywords

Riemannian Manifold Asymptotic Expansion Symmetric Space Heat Kernel Theta Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • Sergio Albeverio
    • 1
  • Teresa Arede
    • 2
    • 3
  1. 1.Mathematisches InstitutRuhr-Universität BochumBochum 1Fed. Rep. Germany
  2. 2.Centre de Physique ThéoriqueCNRS, Luminy, Case 907Marseille Cedex 9France
  3. 3.Faculdade de Engenharia (DEMEC)Universidade do PortoPortoPortugal

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