中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3174-3182.doi: 10.1088/1674-1056/18/8/014

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A rigorous criterion to identify the validity of the Born approximation

李健兵, 王雪松, 王涛   

  1. College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China
  • 收稿日期:2008-11-26 修回日期:2009-01-06 出版日期:2009-08-20 发布日期:2009-08-20
  • 基金资助:
    Project supported by the Explore Foundation of Weapon Development (Grant No 7130620).

A rigorous criterion to identify the validity of the Born approximation

Li Jian-Bing(李健兵)†, Wang Xue-Song(王雪松), and Wang Tao(王涛)   

  1. College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China
  • Received:2008-11-26 Revised:2009-01-06 Online:2009-08-20 Published:2009-08-20
  • Supported by:
    Project supported by the Explore Foundation of Weapon Development (Grant No 7130620).

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摘要： This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.

Abstract: This paper intends to identify the validity of the orn approximation by a new universal criterion, which is ultimately reduced to the calculation of an operator norm. With the purpose of enabling the criterion to be applicable to general scattering problems, a method is proposed to estimate the norm of the operator concerned. Compared with the conventional criterion, this method excels in its ability to acquire a quantificational upper bound of the relative error by Born approximation as well as to extend its valid frequency to a wider range. Two canonical scattering examples are given as evidence for the validity of the criterion.

Key words: electromagnetic scattering, Born approximation, operator theory, relative error

中图分类号:  (Electromagnetic wave propagation; radiowave propagation)

  • 41.20.Jb
03.50.De (Classical electromagnetism, Maxwell equations)