论文标题
软量子波导的光谱特性
Spectral properties of soft quantum waveguides
论文作者
论文摘要
我们考虑了由二维Schrödinger操作员描述的软量子波导，其具有吸引力的潜力，其沿着无限平滑曲线的固定轮廓的形式具有吸引力，该曲线并非笔直，但在合适的意义上是渐近的。使用Birman-Chinginger原理，我们表明，如果定义通道曲线的潜在良好的范围足够狭窄，则此类操作员的离散光谱是非空的。还提到了一些相关问题。
We consider a soft quantum waveguide described by a two-dimensional Schrödinger operators with an attractive potential in the form of a channel of a fixed profile built along an infinite smooth curve which is not straight but it is asymptotically straight in a suitable sense. Using Birman-Schwinger principle we show that the discrete spectrum of such an operator is nonempty if the potential well defining the channel profile is deep and narrow enough. Some related problems are also mentioned.
