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https://doi.org/10.1016/0009-2614(94)00607-5

has been cited by the following article:

• TITLE: Non-Perturbative Treatment of Quantum Mathieu Oscillator

  AUTHORS: Mohammed Janati Idrissi, Abdelaziz Fedoul, Salaheddine Sayouri

  KEYWORDS: Floquet Theorem, Resonating Averages, Mathieu Oscillator, Paul Trap

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.4, April 15, 2020

  ABSTRACT: We study the evolution in time of the quantum Mathieu oscillator (QMO), according to the motion of a charged particle in a radio frequency Paul trap. We adopt non-perturbative treatment based on the quantized Floquet formalism together with the resonating averages method (RAM). We prove that we can develop solutions of the time-dependent Schrödinger equation of such a system, in terms of the simple harmonic oscillator wave functions. Numerical simulations of the analytical results are performed to show the coherence and the squeezed proprieties of the wave-packet of this system.