THE QUADRATIC ZEEMAN EFFECT IN HYDROGEN : AN EXAMPLE OF SEMI-CLASSICAL QUANTIZATION OF A STRONGLY NON-SEPARABLE BUT ALMOST INTEGRABLE SYSTEM

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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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