Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point, II -- Its relevance to the Mathieu equation and the Legendre equation

• 神本, 晋吾

• Kawai, Takahiro

• Takei, Yoshitsugu

抄録

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.

収録刊行物

• Advances in Mathematics

  Advances in Mathematics 260 565-613, 2014-08

  Elsevier Inc.

キーワード

• Exact WKB analysis
• M2P1T operator
• Mathieu equation
• Legendre equation
• Alien derivative
• Microdifferential operator
• Exponential calculus

詳細情報

• CRID: 1050845760724513536
• NII論文ID: 120005462592
• NII書誌ID: AA00513055
• ISSN: 00018708
• HANDLE: 2433/189263
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
  • IRDB
  • CiNii Articles