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Quasi-classical Analysis

  • Stephen J. Gustafson
  • Israel Michael Sigal
Part of the Universitext book series (UTX)

Abstract

In this chapter we investigate the connection between quantum and classical mechanics. More precisely, taking advantage of the fact that the Planck constant provides us with a small parameter, we compute some key quantum quantities — such as quantum energy levels — in terms of relevant classical quantities. This is called quasi-classical (or semi-classical) analysis. To do this, we use the Feynman path integral representation of the evolution operator (propagator) eiHt/ħ. This representation provides a non-rigorous but highly effective tool, as the path integral is expressed directly in terms of the key classical quantity — the classical action.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Stephen J. Gustafson
    • 1
  • Israel Michael Sigal
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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