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.
Received: 26 November 2008
Revised: 06 January 2009
Accepted manuscript online:
Fund: Project supported by the Explore
Foundation of Weapon Development (Grant No 7130620).
Cite this article:
Li Jian-Bing(李健兵), Wang Xue-Song(王雪松), and Wang Tao(王涛) A rigorous criterion to identify the validity of the Born approximation 2009 Chin. Phys. B 18 3174
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
