Abstract

In this paper we revisit the work of Miller and Good, which describes an uniform JWKB type of approximation to the solution of quantum problems. This paper, very well known in atomic physics in the 1970’s 1980’s of the last century, did not attract the same attention from the condensed matter community. Contrary to the usual JWKB approach, Miller and Good’s method yields wave functions that do not diverge at the classical turning points. We apply the method in the context of two-dimensional excitons, an important condensed matter system. In particular, we apply our results to excitons in hexagonal boron nitride, solving the corresponding Wannier equation. We compare the semiclassical results with others from the literature and find good agreement.

Graphic abstract

中文翻译：

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使用Miller和Good的均匀方法在六方氮化硼中的激子能量和波函数

摘要

在本文中，我们回顾了Miller和Good的工作，该工作描述了量子问题解的统一JWKB类型逼近。这篇论文在上世纪1970年代的1980年代的原子物理学中非常著名，但没有引起凝聚态物质界的同样关注。与通常的JWKB方法相反，Miller和Good's方法产生的波动函数在经典转折点处不会发散。我们在二维激子（一种重要的凝聚态系统）的上下文中应用该方法。特别是，我们将结果应用于六方氮化硼中的激子，从而解决了相应的Wannier方程。我们将半经典结果与文献中的其他结果进行比较，并找到良好的一致性。

图形摘要