Scattering for the Schrödinger Equation in Multidimensions. Nonlinear δ-Ewuation, Characterization of Scattering Data and Related Results

Scattering ◽  
2002 ◽  
pp. 1729-1740 ◽  
Author(s):  
R.G. Novikov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Scattering Data

AN INVERSE SCATTERING PROBLEM FOR NONLOCAL POTENTIALS I: THE FAMILY OF PHASE EQUIVALENT WAVEFUNCTIONS

1986 ◽  
Vol 01 (07) ◽  
pp. 449-454 ◽  
Author(s):  
V.M. MUZAFAROV
Keyword(s):  
Integral Equation ◽  
Schrödinger Equation ◽  
Inverse Scattering ◽  
Schrodinger Equation ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattering Data ◽  
The Family ◽  
Consistent Approach ◽  
Nonlocal Potentials

We develop a consistent approach to an inverse scattering problem for the Schrodinger equation with nonlocal potentials. The main result presented in this paper is that for the two-body scattering data, given the problem of reconstructing both the family of phase equivalent two-body wavefunctions and the corresponding family of phase equivalent half-off-shell t-matrices, is reduced to solving a regular integral equation. This equation may be regarded as a generalization of the Gel’fand-Levitan equation.

scholarly journals Characterization of Spectrum and Eigenvectors of the Schrödinger Operator with Chaotic Potentials

2014 ◽  
Vol 15 (2) ◽  
Author(s):  
Weslley Florentino de Oliveira ◽  
Giancarlo Queiroz Pellegrino
Keyword(s):  
Schrödinger Equation ◽  
Schrödinger Operator ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Tight Binding ◽  
System Size ◽  
Schrodinger Operator ◽  
Tight Binding Approximation ◽  
Chaotic Sequences

<em>Chaotic sequences are sequences generated by chaotic maps. A particle moving in a one-dimensional space has its behavior modeled according to the time-independent Schrödinger equation. The tight-binding approximation enables the use of chaotic sequences as the simulation of quantum potentials in the discretized version of the Schrödinger equation. The present work consists of the generation and characterization of spectral curves and eigenvectors of the Schrödinger operator with potentials generated by chaotic sequences, as  well as their comparison with the curves generated by periodic, peneperiodic and random sequences.</em> <em>This comparison is made by calculating in each case the inverse participation ratio as a function of the system size.</em>

Sign in / Sign up

Export Citation Format

Share Document