Robin边界条件是量子力学中的一个普遍问题
Robin boundary conditions are generic in quantum mechanics
摘要：
量子力学中的Robin（或混合）边界条件在过去的二十年里受到了相当大的关注，特别是在纳米尺度系统中的应用。然而，它们的效用在更大的物理学界仍然是模糊的;事实上，人们可以在文献中找到关于特定狄利克雷（或消失）边界条件的假定自然性的现存主张。在这里，我们证明，不仅是Dirichlet边界条件不自然，但罗宾边界条件在长波长近似的短程电位的实用程序。为了说明，我们考虑一个非相对论性粒子在多步和莫尔斯势的影响下，在一维。我们推导出这些潜在的散射和束缚态，并确定参数，描述这些国家在一个有效的系统，即在其中有一个自由粒子的边界。这种方法似乎是普遍适用的，也可推广到许多其他的实际系统。
英文摘要：
Robin (or mixed) boundary conditions in quantum mechanics have received considerable attention in the last two decades, in particular, for applications to nanoscale systems. However, their utility has remained obscure to the larger physics community; in fact, one may find extant claims in the literature about the supposed naturalness of the specific Dirichlet (or vanishing) boundary condition. Here we demonstrate that not only are Dirichlet boundary conditions unnatural, but that Robin boundary conditions have utility in the long-wavelength approximation of short-ranged potentials. For illustration, we consider a non-relativistic particle in one dimension under the influence of the multi-step and Morse potential. We derive the scattering and bound states for these potentials and determine the parameters that describe those states in an effective system, namely one in which there is a free particle with a boundary. This method appears to be generically applicable and also generalizable to many other real systems.
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