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Spring 2010 On the WKB-theoretic structure of a Schrödinger operator with a merging pair of a simple pole and a simple turning point
Shingo Kamimoto, Takahiro Kawai, Tatsuya Koike, Yoshitsugu Takei
Kyoto J. Math. 50(1): 101-164 (Spring 2010). DOI: 10.1215/0023608X-2009-007

Abstract

A Schrödinger equation with a merging pair of a simple pole and a simple turning point (called MPPT equation for short) is studied from the viewpoint of exact Wentzel-Kramers-Brillouin (WKB) analysis. In a way parallel to the case of merging-turning-points (MTP) equations, we construct a WKB-theoretic transformation that brings an MPPT equation to its canonical form (the -Whittaker equation in this case). Combining this transformation with the explicit description of the Voros coefficient for the Whittaker equation in terms of the Bernoulli numbers found by Koike, we discuss analytic properties of Borel-transformed WKB solutions of an MPPT equation.

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Shingo Kamimoto. Takahiro Kawai. Tatsuya Koike. Yoshitsugu Takei. "On the WKB-theoretic structure of a Schrödinger operator with a merging pair of a simple pole and a simple turning point." Kyoto J. Math. 50 (1) 101 - 164, Spring 2010. https://doi.org/10.1215/0023608X-2009-007

Information

Published: Spring 2010
First available in Project Euclid: 13 April 2010

zbMATH: 1201.34141
MathSciNet: MR2629645
Digital Object Identifier: 10.1215/0023608X-2009-007

Subjects:
Primary: 34M60
Secondary: 34E20 , 34M35 , 35A27 , 35A30

Rights: Copyright © 2010 Kyoto University

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Vol.50 • No. 1 • Spring 2010
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