Einstein-Brillouin-Keller quantization

The preceding normal-mode/rigid-rotor sampling assumes the vibrational-rotational levels for the polyatomic reactant are well described by separable normal modes and separability between rotation and vibration. However, if anharmonicities and mode-mode and vibration-rotation couplings are important, it may become necessary to go beyond this approximation and use the Einstein-Brillouin-Keller (EBK) semiclassical quantization conditions [32]... 

The first task is to construct semiclassical wave function in the classically allowed region. As is well known, the KAM torus exists according to the Kolmogorov-Arnold-Moser (KAM) [57,58] and this integral system can be quantized by the Einstein-Brillouin-Keller (EBK) quantization rule [58] as... 

Before 1925/26 quantum mechanics was based on ad hoc quantization procedures such as the Bohr-Sommerfeld quantization method. The disadvantage of this method is that it is coordinate dependent, and usually works only in Cartesian coordinates. In 1917 Einstein suggested a coordinate independent quantization procedure, an important improvement over the Bohr-Sommerfeld quantization scheme. Einstein s quantization method was subsequently extended and improved by Brillouin (1926) and Keller (1958). Therefore, this quantization scheme is referred to as EBK... 

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