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Integral Form of the Fractional Schr
Dong Jianping *
Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, NanJing 210016
*Correspondence author
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Funding: This work was supported by the National Natural Science Foundation of China （No.GrantNo. 11147109）, the Specialized Research Fund for the Doctoral Program of Higher Educationof China （No.Grant No. 20113218120030）, the Fundamental Research Funds for the CentralUniversities （No.Grant No. NS2012119）
Opened online:14 September 2012
Accepted by: none
Citation: Dong Jianping.Integral Form of the Fractional Schr[OL]. [14 September 2012] http://en.paper.edu.cn/en_releasepaper/content/4488917
 
 
The integral form of the 3D space fractional Schr"odinger equationis derived in this paper. Using this integral equation, we study thescattering problems in the fractional quantum mechanics and obtainthe analytical approximate solutions of the wave function and thescattering amplitude using the Born approximation method. The Bornseries, with corrections of every order, is also given. In the end,we discuss the validity of the Born approximation and show thevalidity condition.
Keywords:Applied mathematics; Fractional Schrödinger equation; Riesz fractional derivative; Quantum scattering; Born approximation
 
 
 

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