Critical radius and dipole polarizability for a confined system
Xu Tian (许田)a, Cao Zhuang-Qi (曹庄琪)a, Ou Yong-Cheng (欧永成)a, Shen Qi-Shun (沈启舜)a, Zhu Guo-Long (祝国龙)b
a Institute of Optics and Photonics, Shanghai Jiaotong University, Shanghai 200240, China; b The State Key Laboratory on Fiber-Optic Local Area Networks and Advanced Optical Communication Systems,Shanghai Jiaotong University, Shanghai 200230, China
Abstract The analytical transfer matrix method (ATMM) is applied to calculating the critical radius $r_{\rm c}$ and the dipole polarizability $\alpha_{\rm d}$ in two confined systems: the hydrogen atom and the Hulthén potential. We find that there exists a linear relation between $r_{\rm c}^{1/2}$ and the quantum number $n_{r}$ for a fixed angular quantum number $l$, moreover, the three bounds of $\alpha_{\rm d}$ ($\alpha_{\rm d}^{K}$, $\alpha_{\rm d}^{B}$, $\alpha_{\rm d}^{U}$) satisfy an inequality: $\alpha_{\rm d}^{K}\leq\alpha_{\rm d}^{B}\leq\alpha_{\rm d}^{U}$. A comparison between the ATMM, the exact numerical analysis, and the variational wavefunctions shows that our method works very well in the systems.
Received: 14 September 2005
Revised: 19 March 2006
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No 60237010), Municipal
Scientific and Technological Development Project of Shanghai, China (Grant Nos 012261021 and 01161084) and the Applied Material Research and Development Program of Shanghai, China (Grant No 0111).
Cite this article:
Xu Tian (许田), Cao Zhuang-Qi (曹庄琪), Ou Yong-Cheng (欧永成), Shen Qi-Shun (沈启舜), Zhu Guo-Long (祝国龙) Critical radius and dipole polarizability for a confined system 2006 Chinese Physics 15 1172
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.
