弯曲量子层中的束缚态
Bound States in Curved Quantum Layers
摘要：
我们考虑一个非相对论性量子粒子被约束在一个固定宽度的弯曲层上，该弯曲层建立在一个嵌入$R^3$的非紧表面上。我们假设后者被赋予测地极坐标，并且该层具有硬壁边界。在假设曲面曲率在无穷远处为零的条件下，我们找到了保证几何诱导束缚态存在的充分条件。
英文摘要：
We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in $R^3$. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer has the hard-wall boundary. Under the assumption that the surface curvatures vanish at infinity we find sufficient conditions which guarantee the existence of geometrically induced bound states.
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