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Zbl 0628.70017
Combescure, M.
The quantum stability problem for time-periodic perturbations of the harmonic oscillator. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 47, 63-83 (1987). ISSN 0246-0211

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.
[J.Spicker]

MSC 2000:: *70H99 Hamiltonian and Lagrangian mechanics
81Q15 Perturbation theories for operators and differential equations

Keywords: quantum stability problem; one-dimensional harmonic oscillator; time- periodic operators; infinite diagonal matrices; convergence method; perturbation theory; perturbative stability; quantum mechanical quadrupole radio-frequency trap

Cited in: Zbl 0635.70018

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