管弧的谱和本征函数的数值研究
A numerical study of the spectrum and eigenfunctions on a tubular arc
摘要：
利用微分形式的方法导出了粒子在弯曲纳米管表面上运动的哈密顿量。一个二维的Gram-Schmidt正交归一化过程被用来计算基函数，用于确定具有几百个散射中心的管状弧（双曲余弦形状的纳米管）的本征值和本征态。管的曲率示出诱导依赖于管的曲率参数和弯曲位置的束缚态。
英文摘要：
The Hamiltonian for a particle constrained to move on the surface of a curved nanotube is derived using the methods of differential forms. A two-dimensional Gram-Schmidt orthonormalization procedure is employed to calculate basis functions for determining the eigenvalues and eigenstates of a tubular arc (a nanotube in the shape of a hyperbolic cosine) with several hundred scattering centers. The curvature of the tube is shown to induce bound states that are dependent on the curvature parameters and bend location of the tube.
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