New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in 2D semiclassical asymptotics
S. Yu. Dobrokhotov (1, 2), G. Makrakis (3, 4), V. E., Nazaikinskii (1, 2), T. Ya. Tudorovskii (5) ((1) A. Ishlinsky Institute, for Problems in Mechanics, Moscow, Russia, (2) Moscow Institute of Physics, and Technology, Dolgoprudny, Moscow District, Russia, (3) Department of
TL;DR
This paper introduces a new representation of Maslov's canonical operator near caustics in 2D semiclassical asymptotics using eikonal coordinates, enhancing understanding of wave propagation and quantum mechanics.
Contribution
It proposes a novel formula for Maslov's canonical operator in 2D near caustics utilizing eikonal coordinates, addressing limitations of previous methods.
Findings
New coordinate system simplifies analysis near caustics.
Enhanced formulas improve accuracy of semiclassical approximations.
Specific features of 2D case are elucidated.
Abstract
We suggest a new representation of Maslov's canonical operator in a neighborhood of the caustics using a special class of coordinate systems ("eikonal coordinates") on Lagrangian manifolds. The specific features of the two-dimensional case are considered. The general case is treated in arXiv:1307.2292 [math-ph].
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