A Variational Formulation for Reconstructing Scattering Potential

史小卫; 韩一平; 梁昌洪; 赵瑞金

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A Variational Formulation for Reconstructing Scattering Potential

更新时间：2025-12-08

- A Variational Formulation for Reconstructing Scattering Potential
- Acta Electronica Sinica Issue 3, (1995)
- 作者机构：
  
  西安电子科技大学
- 作者简介：
- 基金信息：
- DOI：
  CLC： O436
- Published：1995
- 稿件说明：
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[1]史小卫,韩一平,梁昌洪,赵瑞金.重建散射位势的变分公式[J].电子学报,1995(03):96-98.

史小卫, 韩一平, 梁昌洪, et al. A Variational Formulation for Reconstructing Scattering Potential[J]. Acta Electronica Sinica, 1995, (3).
[1]史小卫,韩一平,梁昌洪,赵瑞金.重建散射位势的变分公式[J].电子学报,1995(03):96-98. DOI：

史小卫, 韩一平, 梁昌洪, et al. A Variational Formulation for Reconstructing Scattering Potential[J]. Acta Electronica Sinica, 1995, (3). DOI：

摘要

本文研究一维Ｓｃｈｒｏｄｉｎｇｅｒ方程散射位势的重建．从著名的Ｇｅｌ＇ｆａｎｄＬｅｖｉｔａｎ（Ｇ－Ｌ）方程出发，本文构造了一个重建散射位势的变分公式．由于该公式的变分特性，加之它充分利用了Ｇ－Ｌ方程近似解的全部信息，因此能够用于提高一些基于求解Ｇ－Ｌ方程的近似重建方法的计算效率．文中还给出该公式应用于迭代法近似解的一些例子．

Abstract

The reconstruction of scattering potential of one-dimensional Schrodinger equation is studied. A variational formulation is constructed from the famous Gel’fand-Levitan （G-L） equation to reconstruct the scattering potential. Besides its variational property

this formulation has the advantage with which the complete information of the approximation solution of the G-L equation has been fully used. Therefore

it may be used to improve the results of some approximation methods to solve the G-L equation. Some examples are given to illustrate the improvement by applying the formulation to the results of iteration method.

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