修正的吸引性反平方势在感应电偶极子系统中的应用
Modified attractive inverse-square potential in the induced electric dipole system
AI总结：
研究非导电圆柱体内电荷分布，发现修正的吸引性反平方势，含$r^{-1}$附加项，并证明离散能谱的存在。
摘要：
我们研究了具有内半径$r_{0}$的扩展非导电圆柱体内电荷的空间分布。我们的研究揭示了修正的吸引性反平方势的出现，该势源于电场与中性粒子感应电偶极矩之间的复杂相互作用。此修正势显著偏离常规反平方势，展现出与$r^{-1}$成正比的附加项。因此，我们提供了该复杂系统中离散能谱实现的令人信服的证据。
英文摘要：
We examine the spatial distribution of electric charges within an extended, non-conductive cylinder featuring an inner radius denoted as $r_{0}$. Our investigation unveils the emergence of a distinct modified attractive-inverse square potential, arising from the intricate interplay between the electric field and the induced electric dipole moment of a neutral particle. This modified potential notably departs from the conventional inverse-square potential, showcasing an additional term proportional to $r^{-1}$. As a result, we present compelling evidence for the realization of a discrete energy spectrum within this intricate system.
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