无反射作为耦合常数的函数，
Absence of reflection as a function of the coupling constant
摘要：
我们考虑一维方程$-u'' +(Q+ λV) u = 0$的解，其中$Q: \mathbb{R} \to \mathbb{R}$是局部可积的，$V : \mathbb{R} \to \mathbb{R}$与$(V) \subset [0,1]$是可积的，$λ\in \mathbb{R}$是一个耦合常数.给定一族解$\{u_λ \}_{λ\in \mathbb{R}}$满足$u_λ(x) = u_0(x)$，我们证明了$b(λ) := W[u_0, u_λ]$的零点，$u_0$和$u_λ$的朗斯基，形成一个离散集，除非$V \equiv 0$。设置$Q(x) := -E$，可以看到，这个结果的一个特定的结果可以表述为：如果固定能量散射实验$-u'' + λV u = Eu$产生一个反射系数，该反射系数在一组具有聚集点的耦合上消失，则$V \equiv 0$。
英文摘要：
We consider solutions of the one-dimensional equation $-u'' +(Q+ λV) u = 0$ where $Q: \mathbb{R} \to \mathbb{R}$ is locally integrable, $V : \mathbb{R} \to \mathbb{R}$ is integrable with supp$(V) \subset [0,1]$, and $λ\in \mathbb{R}$ is a coupling constant. Given a family of solutions $\{u_λ \}_{λ\in \mathbb{R}}$ which satisfy $u_λ(x) = u_0(x)$ for all $x<0$, we prove that the zeros of $b(λ) := W[u_0, u_λ]$, the Wronskian of $u_0$ and $u_λ$, form a discrete set unless $V \equiv 0$. Setting $Q(x) := -E$, one sees that a particular consequence of this result may be stated as: if the fixed energy scattering experiment $-u'' + λV u = Eu$ gives rise to a reflection coefficient which vanishes on a set of couplings with an accumulation point, then $V \equiv 0$.
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