Observations on the regular and irregular motion as exemplified by the quadratic Zeeman effect and other systems

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Abstract
Recent results of generalised perturbation theory and calculations on the quadratic Zeeman effect spectra are combined to suggest that the first-order integral of the motion recently found using classical degenerate perturbation theory in the weak-field limit are, in fact, approximate integrals over a much larger range of magnetic field strengths. It is shown how this third integral is a consequence of different states being localised in different regions of configuration space rather than being due to any 'hidden symmetries' as has been previously suggested. The inter-relationships between the stabilisation method regular and irregular spectra, unexpectedly localised states, ridge phenomena, assignment of quantum numbers, avoided crossings, extreme motion and adiabatic localisation are also discussed with particular reference to the QZE which is used as an example of these more general ideas.