Non-adiabatic parametric excitation of oscillator-type systems

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Abstract
A harmonic quantum oscillator and the motion of charged particles in a magnetic field have been considered, the dependence on time of the magnetic field and the oscillator frequency being such that they permit us to keep an exact record of non-adiabaticity. For these systems, exact solutions, motion integrals, coherent states and Green functions have been constructed and proper amplitudes and transition probabilities calculated. One of the possible practical applications of the results obtained has been pointed out, namely their use for the interpretation of experiments with electronic vibrational transitions in molecules.