Fundamental solution of the stationary Dirac equation with a linear potential

DOI10.1134/S0040577920120016zbMath1458.81016OpenAlexW3114950634MaRDI QIDQ2229340

I. A. Bogaevskii

Publication date: 23 February 2021

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577920120016

zbMATH Keywords

fundamental solutiongrapheneGreen's matrixparabolic cylinder functionquasiparticlemassless Dirac equationsemiclassical asymptotic behavior

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Spinor and twistor methods applied to problems in quantum theory (81R25) Statistical mechanics of solids (82D20) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Fundamental solutions to PDEs and systems of PDEs with constant coefficients (35E05)

Related Items (1)

Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side

Cites Work

• Caustics of interior scattering
• Front transitions of interior scattering
• On the interior scattering of waves, defined by hyperbolic variational principles
• The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides
• Solution of the two-dimensional Dirac equation with a linear potential and a localized initial condition
• The short-wave asymptotic behaviour of Green's function for the n-dimensional wave equation in an inhomogeneous medium
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