Integral Form of the Fractional Schr¨odinger Equation and Its Application to the Quantum Scattering Problems

摘要

The integral form of the 3D space fractional Schr¨odinger equation is derived in this paper. Using this integral equation, we study the scattering problems in the fractional quantum mechanics and obtain the analytical approximate solutions of the wave function and the scattering amplitude using the Born approximation method. The Born series, with corrections of every order, is also given. In the end, we discuss the validity of the Born approximation and show the validity condition.