论文标题
TBA方程和量化条件
TBA Equations and Quantization Conditions
论文作者
论文摘要
最近已经意识到，在多项式电位的情况下，可以根据TBA方程系统对确切的WKB方法进行重新重新制定。在本文中，我们在各种示例中研究了这种方法。我们由于托莱多而制定了图形程序，该程序提供了一种快速，简单的方法来研究TBA方程的壁缝行为。当与精确的量化条件相辅相成时，TBA方程可用于在量子力学中精确解决光谱问题。我们在许多示例中将量子校正计算为全阶WKB时期，以及许多电位的确切频谱。特别是，我们展示了如何使用该方法来确定无界电势的共振。
It has been recently realized that, in the case of polynomial potentials, the exact WKB method can be reformulated in terms of a system of TBA equations. In this paper we study this method in various examples. We develop a graphical procedure due to Toledo, which provides a fast and simple way to study the wall-crossing behavior of the TBA equations. When complemented with exact quantization conditions, the TBA equations can be used to solve spectral problems exactly in Quantum Mechanics. We compute the quantum corrections to the all-order WKB periods in many examples, as well as the exact spectrum for many potentials. In particular, we show how this method can be used to determine resonances in unbounded potentials.
