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The quantum stability problem for time-periodic perturbations of the harmonic oscillator. (English) Zbl 0628.70017
The quantum stability problem for the one-dimensional harmonic oscillator turbed by time-periodic operators is studied. Starting from perturbations of infinite diagonal matrices by exponentially decaying elements, a convergence method is used to perform perturbation theory. The method is also applied to power law decaying elements, and a perturbative stability result is found. An application to the quantum mechanical quadrupole radio-frequency trap is given.
Reviewer: J.Spicker

MSC:
70H99 Hamiltonian and Lagrangian mechanics
81Q15 Perturbation theories for operators and differential equations in quantum theory
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