HYDROGEN ATOM IN STRONG MAGNETIC FIELDS : REGULAR AND IRREGULAR MOTIONS

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Abstract
The stochastic transition in the classical Hamilton system describing the hydrogen atom in a strong magnetic field is observed by means of Poincaré mappings, and discussed in the framework of the general theory of tori destruction. The existence of the third integral in the regular region below the critical energy can explain the exponentially small separations at avoided crossings of the energy levels, while the stochastic motion above the critical energy accounts for the irregular structure of the spectrum in the inter-n-mixing regime. The regularity of the quasi-Landau resonances corresponds to the existence of the adiabatic invariants above the escape energy

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