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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
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)
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.