Time-dependent scattering on fractal measures

DOI10.1063/1.532494zbMath1024.81050OpenAlexW2053267994MaRDI QIDQ4701642

Charles-Antoine Guerin, Matthias Holschneider

Publication date: 21 November 1999

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

Full work available at URL: https://doi.org/10.1063/1.532494

zbMATH Keywords

wave equationSchrödinger equationwavelet transformtime evolutioninteraction termfractal measuregeneralized multifractal dimensionswavelet correlation dimensionone-dimensional potential scatteringreflected wave packets

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) (2)-body potential quantum scattering theory (81U05) Fractals (28A80)

Related Items

Besov spaces for the Schrödinger operator with barrier potential ⋮ Multiple wave scattering from fractal aggregates ⋮ A representation formula related to Schrödinger operators

Cites Work

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• On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions
• On equivalent definitions of the correlation dimension for a probability measure
• Fractal wavelet dimensions and localization
• Schrödinger operators with singular interactions
• Form perturbations of the Laplacian on L2 (R) by a class of measures
• Perturbation of Schrödinger Hamiltonians by measures—Self-adjointness and lower semiboundedness
• Inverse scattering. I. One dimension
• Inverse scattering on the line
• Analytical properties of scattering amplitudes in one-dimensional quantum theory
• Scattering on fractal measures
• Properties of the 𝑆-matrix of the one-dimensional Schrödinger equation

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