Beyond the WKB approximation in PT-symmetric quantum mechanics
Beyond the WKB approximation in PT-symmetric quantum mechanics
复制标题
超越 PT 对称量子力学中的 WKB 近似
DOI：
10.1088/0305-4470/38/6/010
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
R. Tateo
中科院分区：
文献类型：
--
作者：
P. Dorey;A. Millican;R. Tateo
合并的能级与Bender和Boettcher的模型中的对称性破缺，并在其推广，将离心项，进行了详细分析。即使传统的WKB技术失败，它示出了如何的ODE/IM对应可以被用来获得一个系统的近似方案，捕捉所有以前观察到的功能。非微扰效应起着至关重要的作用，一旦突破临界跃迁通过，几乎所有能级的行为都由非微扰效应控制。此外，径向薛定谔方程的一种新的治疗被用来恢复的本地和非本地的保守电荷在相关的可积量子场论的值，而不需要任何重算，即使角动量是非零的。
The mergings of energy levels associated with the breaking of symmetry in the model of Bender and Boettcher, and in its generalization to incorporate a centrifugal term, are analysed in detail. Even though conventional WKB techniques fail, it is shown how the ODE/IM correspondence can be used to obtain a systematic approximation scheme which captures all previously observed features. Nonperturbative effects turn out to play a crucial role, governing the behaviour of almost all levels once the symmetry-breaking transition has been passed. In addition, a novel treatment of the radial Schrodinger equation is used to recover the values of local and non-local conserved charges in the related integrable quantum field theories, without any need for resummation even when the angular momentum is nonzero.