论文标题
1-D量子谐波振荡器方程的可降低性，并具有无限的振动扰动
Reducibility of 1-d Quantum Harmonic Oscillator Equation with Unbounded Oscillation Perturbations
论文作者
论文摘要
我们根据振荡积分和兰格的转折点理论建立了一个新的估计亲戚。从中我们表明了方程$$ i \ partial_t u = - \ partial_x^2 u+x^2 u+x^2 u+ε\ langle x \ rangle^μW（νx，ωt）u，\ quad u = u = u = u（t，x），〜x \ in \ mathbb r，〜0 \ 0 \ 0 H^1（\ Mathbb r）$ to自主系统对于频率向量$ω$和$ν$的大多数值，其中$ w（φ，θ）$是$ \ Mathbb t^d \ times \ Mathbb t^n $到$ \ $ \ MATHBB R $的平滑地图。
We build a new estimate relative with Hermite functions based upon oscillatory integrals and Langer's turning point theory. From it we show that the equation $$ i \partial_t u =-\partial_x^2 u+x^2 u+ε\langle x\rangle^μ W(νx,ωt)u,\quad u=u(t,x),~x\in\mathbb R,~ 0\leq μ<\frac13,$$ can be reduced in $\mathcal H^1(\mathbb R)$ to an autonomous system for most values of the frequency vector $ω$ and $ν$, where $W(φ, θ)$ is a smooth map from $ \mathbb T^d\times \mathbb T^n$ to $\mathbb R$ and odd in $φ$.
