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The Einstein–Brillouin–Keller method is a quantization rule going from classical mechanics to quantum mechanics, according to wikipedia:

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I have several question regarding the above description:

  1. what does it mean that a pair $(q_i, p_i)$ describes a closed function or a periodic function in $q_i$.

  2. what does $\mu_i$ and $b_i$ really mean, how to determine them in different systems.

I hope the answer can be as detailed as possible, better still, explain using different (elementary) examples, for example harmonic oscillator, particle in magnetic field, etc, to illustrate all the basic points of the above formula and question.

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