关键词: Schrodinger方程, 散射问题, PML方法

Abstract: We discussed the numerical computation of the scattering problems for twodimensional Schrodinger equation (-Δ+V(x)-k²)u=0. For a class of specific potentials, i.e., V(r)=b/r^δ outside a circular domain B_r0, where both b>0 and δ>1 are constants, we presented a PML method. We first got the PML equationsby making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Garding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experimentswhich show that this method is feasible to a certain extent.

Key words: Schrodinger equations, scattering problems, PML method