Semi-Classical Theory — Path Integrals

  • L. E. Reichl
Part of the Institute for Nonlinear Science book series (INLS)


The “Old Quantum Theory” which is based on the Bohr-Sommerfeld quantization condition, provided a means of quantizing a classical mechanical system by quantizing the action variables associated with invariant tori. (For a historical discussion see [Born 1960].) However, it was recognized by Einstein, as early as 1917 [Einstein 1917], that this method could only be used for systems in which trajectories lie on invariant tori. The Bohr-Sommerfeld quantization condition could not be used to quantize chaotic systems and until recently no method existed by which to connect classically chaotic systems with their quantum counterpart.


Periodic Orbit Chaotic System Path Integral Trace Formula Conjugate Point 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • L. E. Reichl
    • 1
  1. 1.Center for Statistical Mechanics and Complex Systems, Department of PhysicsUniversity of Texas at AustinAustinUSA

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