形变表面上的曲率诱导量子势
Curvature induced quantum potential on deformed surfaces
摘要：
我们研究曲率对量子粒子在表面上运动的影响。对于高斯凸块，我们推导并讨论了量子势，它导致了角动量为零的粒子出现束缚态。高斯凹凸提供了问题的特征长度。为了完整性，我们提出了一个微分几何中的反问题，即什么变形的表面产生规定的曲率诱导量子势。我们解决这个逆问题的情况下，旋转曲面。我们还表明，存在旋转表面的形式，一个圆形带的对称轴，允许粒子与通用角动量绑定。
英文摘要：
We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface. For the Gaussian bump we derive and discuss the quantum potential which results in the appearance of a bound state for particles with vanishing angular momentum. The Gaussian bump provides a characteristic length for the problem. For completeness we propose an inverse problem in differential geometry, i.e. what deformed surfaces produce prescribed curvature induced quantum potentials. We solve this inverse problem in the case of rotational surfaces. We also show that there exist rotational surfaces in the form of a circular strip around the axis of symmetry which allow particles with generic angular momentum to bind.
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