On the complex WKB analysis for a second order linear O.D.E. with a many-segment characteristic polygon
type: Item
instance of: scholarly article
title: On the complex WKB analysis for a second order linear O.D.E. with a many-segment characteristic polygon
zbMATH Open document ID: 1082.34081
author: Minoru Nakano
published in: Tokyo Journal of Mathematics
publication date: 2005-03-14T00:00:00Z
review text: This paper concerns the one-dimensional Schrödinger equation \[ \varepsilon^{2h}{d^2y\over dx^2}= Q(x,\varepsilon) y,\quad Q(x,\varepsilon):= \sum^h_{j=0} a_j\varepsilon^j x^{m_j}; \] \[ m_j:= {(h- j+1)(h-j)\over 2},\quad 0\neq a_j\in\mathbb C\;\forall j, \] \[ h= 2,3,4,\dots;\quad x,y\in\mathbb{C};\quad 0< \varepsilon\leq \varepsilon_0;\quad D: 0\leq|x|\leq x_0. \] The asymptotic behavior at the turning point \(x= 0\) is studied when the characteristic polygon has many segments.
reviewed by: Masaaki Yoshida
Mathematics Subject Classification ID: 34M60
Mathematics Subject Classification ID: 34E20
zbMATH DE Number: 2145301
zbMATH Keywords: WKB analysis
zbMATH Keywords: turning point
zbMATH Keywords: Stokes curve
zbMATH Keywords: characteristic polygon
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1244208399
OpenAlex ID: W1989186671
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DOI: 10.3836/TJM/1244208399
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description: scientific article; zbMATH DE number 2145301