Uniformization of WKB functions by Wigner transform

DOI10.1080/00036811.2013.794939zbMath1302.34088OpenAlexW2012814981WikidataQ58177680 ScholiaQ58177680MaRDI QIDQ5417863

G. N. Makrakis, S. K. Giannopoulou

Publication date: 22 May 2014

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2013.794939

zbMATH Keywords

causticsgeometric opticsWigner transformuniform stationary phase

Mathematics Subject Classification ID

Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Asymptotic expansions of solutions to ordinary differential equations (34E05) Multiple scale methods for ordinary differential equations (34E13) Geometric optics (78A05)

Related Items (1)

Quantum curves as quantum distributions

Cites Work

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• The Wigner function of two dimensional tori: Uniform approximation and projections
• Quasiclassical approximation in stationary scattering problems
• The Van Vleck formula, Maslov theory, and phase space geometry
• On the evolution of the semi-classical Wigner function in higher dimensions
• Semi-classical mechanics in phase space: A study of Wigner’s function
• Homogenization limits and Wigner transforms
• Semiclassical Wigner Function and Geometrical Optics
• On the Theory of Complex Rays
• The high‐frequency asymptotic field of a point source in an inhomogeneous medium

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