Semiclassical representation of the scattering matrix by a Feynman integral

DOI10.1007/s002200050483zbMath0920.34069OpenAlexW2025455675MaRDI QIDQ1287117

Setsuro Fujiié

Publication date: 23 September 1999

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002200050483

zbMATH Keywords

scattering problemtunneling effectsFeynman integralclassical trajectoriesone-dimensional Schrödinger equationsexact WKB method

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (6)

Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach ⋮ Breit–Wigner formula at barrier tops ⋮ Transition probability for multiple avoided crossings with a small gap through an exact WKB method and a microlocal approach ⋮ Landau-Zener formula in a ``non-adiabatic regime for avoided crossings ⋮ Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg—de Vries equation in the small‐dispersion limit ⋮ Feynman-type representation of the scattering matrix on the line via a discrete-time quantum walk

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