Radiation conditions for the difference schrödinger operators
Radiation conditions for the difference schrödinger operators
复制标题
差分薛定谔算子的辐射条件
DOI：
10.1080/00036810108841007
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发表时间：
2001
影响因子：
1.1
通讯作者：
B. Vainberg
中科院分区：
文献类型：
--
作者：
W. Shaban;B. Vainberg
考虑确定格子上薛定谔方程唯一解的问题，其中Δ是拉普拉斯差值，f和q都有有限支持。结果表明，即使对于未受扰动的算子 (q(x)=0)，也存在极限吸收原理失效的特殊点集 So。该异常集合由 d 为偶数时和 d 为奇数时的点组成。对于 的所有值，找到了与由极限吸收原理确定的问题相同的解决方案的辐射条件。这些解是以不同频率传播的多个波的组合，波的数量取决于 λ 的值。
The problem of determining a unique solution of the Schrödinger equation on the lattice is considered, where Δ is the difference Laplacian and both f and q have finite supports. It is shown that there is an exceptional set So of points on for which the limiting absorption priciple fails, even for unperturbed operator (q(x)=0). This exceptional set consists of the points when d is even and when d is odd. For all Values of , the radiation conditions are found which single out the same solutions of the problem as the ones determined by the limiting absorption principle. These solutions are conbinations of several waves propagating with different frequencies, and the number of waves depends on the value of λ.