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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Analytical treatment of Schrodinger problems with geometrical perturbations
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Analytical treatment of Schrodinger problems with geometrical perturbations

机译：带几何扰动的薛定inger问题的解析处理

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摘要

An analytical theory for calculating shifts in eigenvalues to Schrodinger problems due to geometrical perturbations is proposed. The possibility of growing practically any nano-heterostructure today makes it interesting to examine the influence of shape and size on, e. g., electronic, optical and magnetic properties. For that, detailed knowledge of shifts in eigenvalues induced by changes in geometry, either intentionally or unintentionally, is important. Several examples are presented so as (a) to verify the geometry-perturbative model against exact calculations and (b) to attack problems which cannot be solved exactly without resorting to numerical partial differential equation (PDE) techniques. The latter include the cases of a particle confined to a three-dimensional cylinder with a sinusoidally varying radius as a function of the axial coordinate in the presence (or absence) of a dc electric field along the cylinder axis.
机译：提出了一种解析理论，用于计算由于几何扰动而导致的特征值向薛定inger问题的偏移。今天，几乎可以生长任何纳米异质结构的可能性使得研究形状和尺寸对例如纳米线的影响非常有趣。例如，电子，光学和磁性。为此，重要的是，有意或无意地了解由几何形状变化引起的特征值变化的详细知识。给出了几个示例，以便（a）对照精确的计算来验证几何微扰模型，以及（b）攻击无法依靠数字偏微分方程（PDE）技术无法精确解决的问题。后者包括在沿圆柱轴存在（或不存在）直流电场的情况下，粒子受限于三维圆柱体的情况，该圆柱体的正弦变化半径是轴向坐标的函数。

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