Semiclassical Theory—Path Integrals
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 KAM tori. (For a historical discussion, see [Born I960].) 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 to connect classically chaotic systems with their quantum counterpart.
KeywordsPeriodic Orbit Chaotic System Absorption Cross Section Trace Formula Conjugate Point
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