On the WKB-theoretic structure of a Schrödinger operator with a merging pair of a simple pole and a simple turning point

DOI10.1215/0023608X-2009-007zbMath1201.34141OpenAlexW1972221978MaRDI QIDQ974788

Yoshitsugu Takei, Shingo Kamimoto, Tatsuya Koike, Takahiro Kawai

Publication date: 7 June 2010

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/0023608x-2009-007

Mathematics Subject Classification ID

Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (8)

Shatalov-Sternin's construction of complex WKB solutions and the choice of integration paths ⋮ On singular solutions to PDEs with turning point involving a quadratic nonlinearity ⋮ On the exact WKB analysis of higher order simple-pole type operators ⋮ Topological recursion and uncoupled BPS structures. II: Voros symbols and the \(\tau\)-function ⋮ Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point. I: Its WKB-theoretic transformation to the Mathieu equation ⋮ On the WKB theoretic transformation to the boosted Airy equation ⋮ On the Voros coefficient for the Whittaker equation with a large parameter -- some progress around Sato's conjecture in exact WKB analysis ⋮ Resurgence and holomorphy: From weak to strong coupling

Cites Work

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• On the Voros coefficient for the Whittaker equation with a large parameter -- some progress around Sato's conjecture in exact WKB analysis
• Voros resurrection and periods of hyperelliptic curves
• First steps in ``calcul étrange
• Microlocal reduction of ordinary differential operators with a large parameter
• On the exact WKB analysis of second order linear ordinary differential equations with simple poles
• Exact semiclassical expansions for one-dimensional quantum oscillators

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