论文标题
软量子波导具有显式切割局
Soft quantum waveguides with an explicit cut-locus
论文作者
论文摘要
我们考虑二维Schroedinger操作员，具有沿无界曲线构建的固定轮廓通道的形式具有吸引力的潜力，该曲线由圆形弧和两个直线半线组成。利用曲线切割局部外部的平行坐标的测试函数参数，我们确定了离散特征值的存在。这是在非平滑情况下以及不需要非阳性约束势的不同技术中Exner最近结果的特殊变体。
We consider two-dimensional Schroedinger operators with an attractive potential in the form of a channel of a fixed profile built along an unbounded curve composed of a circular arc and two straight semi-lines. Using a test-function argument with help of parallel coordinates outside the cut-locus of the curve, we establish the existence of discrete eigenvalues. This is a special variant of a recent result of Exner in a non-smooth case and via a different technique which does not require non-positive constraining potentials.
