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We study the evolution of the energy and magnetic moment of a quantum chargedparticle placed in a homogeneous magnetic field, when this field changesadiabatically its sign. We show that after a single magnetic field passagethrough zero value, the famous adiabatic invariant ratio of energy to frequencyis reestablished again, but with the proportionality coefficient higher than inthe initial state. The concrete value of this proportionality coefficientdepends on the power index of the frequency dependence on time near zero point.In particular, the adiabatic ratio of the initial ground state (with zeroradial and angular quantum numbers) triplicates if the frequency tends to zerolinearly as function of time. If the Larmor frequency attains zero more thanonce, the adiabatic proportionality coefficient strongly depends on the lengthsof the time intervals between zero points, so that the mean energy behavior canbe quasi-stochastic after many passages through zero value. The originalBorn-Fock adiabatic theorem does not work after the frequency passes throughzero. However, its generalization is found: the initial Fock state becomes awide superposition of many instantaneous Fock states, whose weights do notdepend on time in the new adiabatic regime.

Adiabatic amplification of energy and magnetic moment of a charged particle after the magnetic field inversion