A nonrelativistic scalar particle moving on a curved surface undergoes a geometric scattering whose behavior is sensitive to the theoretically ambiguous values of the intrinsic and extrinsic curvature coefficients entering the expression for the quantum Hamiltonian operator. This suggests using the scattering data to settle the ambiguity in the definition of the Hamiltonian. It has recently been shown that the inclusion of point defects on the surface enhances the geometric scattering effects. We perform a detailed study of the geometric scattering phenomenon in the presence of line defects for the case that the particle is confined to move on a Gaussian bump and the defect(s) are modeled by delta function potentials supported on a line or a set of parallel lines normal to the scattering axis. In contrast to a surface having point defects, the scattering phenomenon associated with this system is generically geometric in nature in the sense that for a flat surface, the scattering amplitude vanishes for all scattering angles \(\theta \) except \(\theta =\theta _0\) and \(\pi -\theta _0\), where \(\theta _0\) is the angle of incidence. We show that the presence of the line defects amplifies the geometric scattering due to the Gaussian bump. This amplification effect is particularly strong when the center of the bump is placed between two line defects.

在曲面上移动的非相对论标量粒子会经历几何散射，其行为对输入汉密尔顿量子算子的本征和非本征曲率系数的理论上不明确的值敏感。这建议使用散射数据来解决哈密顿量定义中的歧义。最近显示出在表面上包含点缺陷会增强几何散射效果。我们对存在线缺陷的情况下的几何散射现象进行了详细的研究，例如当粒子被限制在高斯凸点上移动并且缺陷是由一条或一组线所支持的增量函数势建模时垂直于散射轴的平行线。与具有点缺陷的表面相反，\（\ theta \）除了\（\ theta = \ theta _0 \）和\（\ pi-\ theta _0 \）之外，其中\（\ theta _0 \）是入射角。我们表明，由于高斯凸点，线缺陷的存在会放大几何散射。当凸块的中心位于两条线缺陷之间时，这种放大效果特别强。