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.