Abstract
Semi-classical quantization of multidimensional systems is discussed both in terms of the Einstein-Brillouin-Keller quantization on invariant tori, and in terms of infinite families of periodic orbits. The notions of separability, integrability, and non-integrability of classical systems are introduced. An approximate integrability is used to quantize the quadratic Zeeman problem, via analytic calculation of the Birkhoff-Gustavson normal form.
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