The Matrix Schrödinger Equation and the Characterization of the Scattering Data

2020 ◽  
pp. 19-47
Author(s):  
Tuncay Aktosun ◽  
Ricardo Weder
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Scattering Data ◽  
The Matrix

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.

ALGEBRAIC APPROACH TO THE PSEUDOHARMONIC OSCILLATOR IN 2D

2002 ◽  
Vol 11 (02) ◽  
pp. 155-160 ◽  
Author(s):  
SHI-HAI DONG ◽  
ZHONG-QI MA
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Algebraic Approach ◽  
Matrix Elements ◽  
Ladder Operators ◽  
Commutation Relations ◽  
The Matrix ◽  
Pseudoharmonic Oscillator ◽  
Analytical Expressions

A realization of the ladder operators for the solutions to the Schrödinger equation with a pseudoharmonic oscillator in 2D is presented. It is shown that those operators satisfy the commutation relations of an SU(1, 1) algebra. Closed analytical expressions are evaluated for the matrix elements of some operators r2 and r∂/∂ r

scholarly journals Linear Barycentric Rational Method for Solving Schrodinger Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Peichen Zhao ◽  
Yongling Cheng
Keyword(s):  
Schrödinger Equation ◽  
Convergence Rate ◽  
Collocation Method ◽  
Schrodinger Equation ◽  
Interpolation Method ◽  
Rational Interpolation ◽  
Barycentric Interpolation ◽  
Rational Polynomial ◽  
The Matrix ◽  
Barycentric Rational Interpolation

A linear barycentric rational collocation method (LBRCM) for solving Schrodinger equation (SDE) is proposed. According to the barycentric interpolation method (BIM) of rational polynomial and Chebyshev polynomial, the matrix form of the collocation method (CM) that is easy to program is obtained. The convergence rate of the LBRCM for solving the Schrodinger equation is proved from the convergence rate of linear barycentric rational interpolation. Finally, a numerical example verifies the correctness of the theoretical analysis.

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