scholarly journals Born Approximation in One‐Dimensional Scattering Problems

1967 ◽  
Vol 42 (5) ◽  
pp. 1200-1200
Author(s):  
Charles Soodak ◽  
Mark Harrison
Keyword(s):  
Born Approximation ◽  
Scattering Problems ◽  
One Dimensional

One-Dimensional Jost Solutions: The S-Matrix Revisited

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Boundary Conditions ◽  
Transmission Coefficient ◽  
Radial Equation ◽  
Scattering Problems ◽  
One Dimensional ◽  
S Matrix ◽  
Jost Functions ◽  
Jost Solutions ◽  
Square Well ◽  
Matrix Problems

This chapter examines the properties of one-dimensional Jost solutions for S-matrix problems. It first considers how the left–right transmission and reflections coefficients can be expressed in terms of the elements of the S-matrix for one-dimensional scattering problems on, focusing on poles of the transmission coefficient. It then uses the radial equation to revisit the problem of the square-well potential from the perspective of the Jost solution, with Jost boundary conditions at r = 0 and as r approaches infinity. It also presents the notations for the Jost functions and the S-matrix before discussing the problem of scattering from a constant spherical inhomogeneity.

Modified Born approximation for solving scattering problems

2003 ◽  
Vol 113 (4) ◽  
pp. 2284-2284 ◽  
Author(s):  
Igor L. Oboznenko ◽  
Vladimir Genis ◽  
Dat H. Tran
Keyword(s):  
Born Approximation ◽  
Scattering Problems

scholarly journals Geometric reconstruction of flaws by one‐dimensional inverse Born approximation

1982 ◽  
Vol 72 (S1) ◽  
pp. S105-S106
Author(s):  
D. K. Hsu ◽  
James H. Rose ◽  
R. B. Thompson ◽  
D. O. Thompson
Keyword(s):  
Born Approximation ◽  
One Dimensional ◽  
Geometric Reconstruction

scholarly journals A TWO-GRID TIME-DEPENDENT FORMALISM FOR THE MAXWELL EQUATION

2003 ◽  
Vol 02 (04) ◽  
pp. 537-546 ◽  
Author(s):  
DANIEL NEUHAUSER ◽  
ROI BAER
Keyword(s):  
Maxwell Equations ◽  
Three Dimensional ◽  
Reaction Dynamics ◽  
Iterative Solution ◽  
Time Dependent ◽  
Scattering Problems ◽  
One Dimensional ◽  
Initial Wave ◽  
Chemical Reaction Dynamics ◽  
Iterative Solutions

We develop a formalism for efficient iterative solutions of scattering problems involving the Maxwell equations. The methods, borrowed from recent advancements in chemical reaction dynamics, represent the scattering wavefunctions on two grids; one used for the initial wave and is one-dimensional; the other is a small three-dimensional grid padded with absorbing-potentials on which the scattered function is represented. The formalism is automatically suitable for scattering studies of transmission, reflection and scattering components of a wave. The simulations can be done with time-dependent wavepackets or direct iterative solution for the Green's function, but the results are rigorous time-independent (frequency-dependent) scattering amplitudes. Model time-dependent simulations involving up to a 100×100×100 grid for the inner wavefunction were numerically done on a simple PC.

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