Author(s)

Mohammed Janati Idrissi, Abdelaziz Fedoul, Salaheddine Sayouri

Laboratory of Theoretical and Applied Physics, Faculty of Sciences Dhar Al Mahraz, University of Sidi Mohamed Ben Abdel-lah, Fez, Morocco.

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.

Floquet Theorem, Resonating Averages, Mathieu Oscillator, Paul Trap

Idrissi, M. , Fedoul, A. and Sayouri, S. (2020) Non-Perturbative Treatment of Quantum Mathieu Oscillator. Journal of Applied Mathematics and Physics, 8, 698-709. doi: 10.4236/jamp.2020.84054.