Conservation equations for the semiclassical Schrödinger equation near caustics

DOI10.1080/00036810701355000zbMath1146.35022OpenAlexW2075742293MaRDI QIDQ5442936

G. N. Makrakis, Evagelia Kalligiannaki

Publication date: 18 February 2008

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

Full work available at URL: https://doi.org/10.1080/00036810701355000

zbMATH Keywords

geometrical opticsWigner transformhighly oscillatory initial data

Mathematics Subject Classification ID

Asymptotic expansions of solutions to PDEs (35C20) 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) Initial value problems for linear higher-order PDEs (35G10) Geometric optics (78A05) Asymptotic behavior of solutions to equations on manifolds (58K55)

Cites Work

• Unnamed Item
• An integral representation for the product of Airy functions
• Multi-phase computations of the semiclassical limit of the Schrödinger equation and related problems: Whitham vs Wigner
• On the evolution of the semi-classical Wigner function in higher dimensions
• Milestones in mathematical physics Noether's theorem
• Invariant variation problems
• Semiclassical Wigner Function and Geometrical Optics
• On the Quantum Correction For Thermodynamic Equilibrium
• The Quantum Theory of Motion

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