Reducibility of 1-d Quantum Harmonic Oscillator Equation with Unbounded Oscillation Perturbations

2020/03/29 by Liang, Zhenguo, Luo, Jiawen · 1 citation
#35J10 #37K55 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2003.12951

Abstract

We build a new estimate relative with Hermite functions based upon oscillatory integrals and Langer's turning point theory. From it we show that the equation i ∂_t u =-∂_x² u+x² u+ε⟨ x⟩^μ W(νx,ωt)u, u=u(t,x),~x∈\mathbb R,~ 0≤ μ

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• On the reducibility of the 1d quantum harmonic oscillator with a quasi-periodic bounded potential

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