论文标题
1-dSchrödinger方程可降低，并具有无限的振荡扰动
Reducibility of 1-d Schrödinger equation with unbounded oscillation perturbations
论文作者
论文摘要
我们根据振荡性积分和Langer的转折点方法，为操作员$ - \ partial_ {xx}+\ Mathcal V（x）$的正常特征函数构建了一个新的估计。从中及提高的可降低定理我们显示了方程\ [\ textStyle {\ rm i} \partial_tψ= - \ partial_x^2ψ+\ mathcal v（x）ψ+ε\ langle x \ rangle x \ rangle^μw（νx，ωt，ωt）ψ，\ quadψ= quadψ=ψ（t，x） 〜μ <\ min \ left \ {\ ell- \ frac23，\ frac {\ sqrt {\ sqrt {4 \ ell^2-2 \ ell^2-2 \ ell+1} -1} 2 \ right \}，可以减少$ l^2（\ nathbb r）$ y Mathbb $ $ $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n of \}] ϕ）$是$ \ Mathbb t^d \ times \ Mathbb t^n $到$ \ MATHBB r $和odd $φ$中的平滑地图。
We build a new estimate for the normalized eigenfunctions of the operator $-\partial_{xx}+\mathcal V(x)$ based on the oscillatory integrals and Langer's turning point method, where $\mathcal V(x)\sim |x|^{2\ell}$ at infinity with $\ell>1$. From it and an improved reducibility theorem we show that the equation \[\textstyle {\rm i}\partial_t ψ=-\partial_x^2 ψ+\mathcal V(x) ψ+ε\langle x\rangle^μ W(νx,ωt)ψ,\quad ψ=ψ(t,x),~x\in\mathbb R, ~μ<\min\left\{\ell-\frac23,\frac{\sqrt{4\ell^2-2\ell+1}-1}2\right\},\] can be reduced in $L^2(\mathbb R)$ to an autonomous system for most values of the frequency vector $ω$ and $ν$, where $W(φ, ϕ)$ is a smooth map from $ \mathbb T^d\times \mathbb T^n$ to $\mathbb R$ and odd in $φ$.
