scholarly journals Scattering Theory with Finite-Gap Backgrounds: Transformation Operators and Characteristic Properties of Scattering Data

2012 ◽  
Vol 16 (2) ◽  
pp. 111-136 ◽  
Author(s):  
Iryna Egorova ◽  
Johanna Michor ◽  
Gerald Teschl
Keyword(s):  
Scattering Theory ◽  
Scattering Data

scholarly journals A duality between scattering poles and transmission eigenvalues in scattering theory

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200612
Author(s):  
Fioralba Cakoni ◽  
David Colton ◽  
Houssem Haddar
Keyword(s):  
Numerical Method ◽  
Scattering Theory ◽  
Scattering Problem ◽  
Scattering Data ◽  
Scattering Operator ◽  
Unified Approach ◽  
Transmission Eigenvalues ◽  
Dirichlet Eigenvalues ◽  
Scattered Fields

In this paper, we develop a conceptually unified approach for characterizing and determining scattering poles and interior eigenvalues for a given scattering problem. Our approach explores a duality stemming from interchanging the roles of incident and scattered fields in our analysis. Both sets are related to the kernel of the relative scattering operator mapping incident fields to scattered fields, corresponding to the exterior scattering problem for the interior eigenvalues and the interior scattering problem for scattering poles. Our discussion includes the scattering problem for a Dirichlet obstacle where duality is between scattering poles and Dirichlet eigenvalues, and the inhomogeneous scattering problem where the duality is between scattering poles and transmission eigenvalues. Our new characterization of the scattering poles suggests a numerical method for their computation in terms of scattering data for the corresponding interior scattering problem.

scholarly journals Quantum diffraction grating: A possible new description of nuclear elastic scattering

2016 ◽  
Vol 25 (02) ◽  
pp. 1650008 ◽  
Author(s):  
H. Wojciechowski
Keyword(s):  
Elastic Scattering ◽  
Diffraction Grating ◽  
Scattering Theory ◽  
Generalized Functions ◽  
Scattering Data ◽  
Quantum Scattering ◽  
Nuclear Scattering ◽  
Quantum Diffraction ◽  
Polynomial Series ◽  
Elastic Differential Cross Section

The problem of discontinuous functions and their representations in the form of Legendre polynomial series in quantum nuclear scattering theory is presented briefly. The problem is quite old yet not adequately explained in numerous Quantum Theory textbooks and sometimes not correctly understood by physicists. Introduction of the generalized functions into the quantum scattering theory clarifies the problem and allows to propose new interpretations of nuclear elastic scattering phenomenon. The derived new forms of the full elastic scattering amplitudes and possibility of splitting them suggest existence of dynamical quantum diffraction grating around the nuclei. Particularly important fact is that this grating existing in the space around the nucleus makes considerable contribution to the experimental elastic differential cross-section. All these might be quite important in analyses of nuclear elastic scattering data and so require to be stated in a more detailed and clear way.

An inverse problem of scattering theory for the perturbed Stark operator on the semiaxis

2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Aynur R. Ahmedova
Keyword(s):  
Inverse Problem ◽  
Scattering Theory ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Scattering Data ◽  
Stark Operator ◽  
Necessary And Sufficient

AbstractIn the present paper, we consider the inverse problem for the perturbed Stark operator. We obtain necessary and sufficient conditions on the set of values, which could serve as scattering data for the considered operator, and we prove their sufficiency.

scholarly journals Scattering Theory for 2N Parameter Models of Finitely Many Relativistic δ-Sphere and δ-Sphere plus Coulomb Interactions Supported by Concentric Spheres in Quantum Mechanics

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
A. Vyabandi ◽  
J. Shabani
Keyword(s):  
Quantum Mechanics ◽  
Scattering Theory ◽  
Spectral Properties ◽  
Scattering Data ◽  
Coulomb Interactions ◽  
Resolvent Equations ◽  
Concentric Spheres ◽  
Mathematical Definitions

We study scattering theory for 2N parameter models of finitely many relativistic δ-sphere and δ-sphere plus Coulomb interactions. We provide the mathematical definitions of the Hamiltonians, solve the resolvent equations, and compute the nonrelativistic limits for both models. We obtain new results related to spectral properties and scattering data.

Southern Hemisphere Seti Survey: Five Years of Project Meta II

1997 ◽  
Vol 161 ◽  
pp. 611-621
Author(s):  
Guillermo A. Lemarchand ◽  
Fernando R. Colomb ◽  
E. Eduardo Hurrell ◽  
Juan Carlos Olalde
Keyword(s):  
Southern Hemisphere ◽  
Scattering Theory ◽  
Galactic Plane ◽  
Narrow Band ◽  
Neutral Hydrogen ◽  
Sky Survey ◽  
Inertial Frames ◽  
Interstellar Scattering ◽  
Extraterrestrial Origin ◽  
Spectral Channels

AbstractProject META II, a full sky survey for artificial narrow-band signals, has been conducted from one of the two 30-m radiotelescopes of the Instituto Argentino de Radioastronomía (IAR). The search was performed near the 1420 Mhz line of neutral hydrogen, using a 8.4 million channels Fourier spectrometer of 0.05 Hz resolution and 400 kHz instantaneous bandwidth. The observing frequency was corrected both for motions with respect to three astronomical inertial frames, and for the effect of Earths rotation, which provides a characteristic changing signature for narrow-band signals of extraterrestrial origin. Among the 2 × 1013spectral channels analyzed, 29 extra-statistical narrow-band events were found, exceeding the average threshold of 1.7 × 10−23Wm−2. The strongest signals that survive culling for terrestrial interference lie in or near the galactic plane. A description of the project META II observing scheme and results is made as well as the possible interpretation of the results using the Cordes-Lazio-Sagan model based in interstellar scattering theory.

Dynamical Scattering in Electron Diffraction of wet Protein Crystals

1980 ◽  
Vol 38 ◽  
pp. 42-43
Author(s):  
B. B. Chang ◽  
D. F. Parsons
Keyword(s):  
Electron Diffraction ◽  
Scattering Theory ◽  
Protein Crystals ◽  
Electron Diffraction Data ◽  
Specimen Thickness ◽  
Major Question ◽  
X Ray ◽  
Scattering Effects ◽  
Diffraction Patterns ◽  
Acceleration Voltage

The significance of dynamical scattering effects remains the major question in the structural analysis by electron diffraction of protein crystals preserved in the hydrated state. In the few cases (single layers of purple membrane and 400-600 Å thick catalase crystals examined at 100 kV acceleration voltage) where electron-diffraction patterns were used quantitatively, dynamical scattering effects were considered unimportant on the basis of a comparison with x-ray intensities. The kinematical treatment is usually justified by the thinness of the crystal. A theoretical investigation by Ho et al. using Cowley-Moodie multislice formulation of dynamical scattering theory and cytochrome b5as the test object2 suggests that kinematical analysis of electron diffraction data with 100-keV electrons would not likely be valid for specimen thickness of 300 Å or more. We have chosen to work with electron diffraction patterns obtained from actual wet protein crystals (rat hemoglobin crystals of thickness range 1000 to 2500 Å) at 200 and 1000 kV and to analyze these for dynamical effects.

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