Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point. I& II
Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point. I& II
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具有两个简单极点和一个简单转折点 I 和 II 的合并三元组的薛定谔方程的精确 WKB 分析。
DOI：
10.1016/j.aim.2014.02.028
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发表时间：
2014
影响因子：
1.7
通讯作者：
T. Kawai and Y. Takei
中科院分区：
文献类型：
--
作者：
S. Kamimoto;T. Kawai and Y. Takei
我们发展了M2P1T(合并两个简单极点和一个简单转折点)薛定谔方程的精确WKB分析。在第二部分中，利用对第一部分中构造的代数Mathieu方程的WKB理论变换，通过对Legendre方程的Borel变换的WKB解的分析，我们计算了它的Borel变换的WKB解在每个与简单极点相关的固定奇点上的外来导数。在奇异导数的计算过程中，我们充分利用了微微分算子，它的符号由出现在代数Mathieu方程和Legendre方程的系数中的无穷级数给出。
We develop the exact WKB analysis of an M2P1T (merging two simple poles and one simple turning point) Schrödinger equation. In Part II, using a WKB-theoretic transformation to the algebraic Mathieu equation constructed in Part I, we calculate the alien derivative of its Borel transformed WKB solutions at each fixed singular point relevant to the simple poles through the analysis of Borel transformed WKB solutions of the Legendre equations. In the course of the calculation of the alien derivative we make full use of microdifferential operators whose symbols are given by the infinite series that appear in the coefficients of the algebraic Mathieu equation and the Legendre equation.