Abstract
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.
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Reichl, L.E. (2004). Semiclassical Theory—Path Integrals. In: The Transition to Chaos. Institute for Nonlinear Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4350-0_8
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