The FFT-symplectic integrator (SI) scheme devised for solving the wave packet propagation problem is applied to stationary reactive-scattering problems. In order to relate the stationary problem to the time-dependent problem, a class of Schrodinger equation with an inhomogeneous wave source term is;introduced. By using the equivalence between the stationary scattering eigenstate and the equilibrium state of the inhomogeneous Schrodinger equation, the scattering eigenstates can be computed by integrating-the inhomogeneous Schrodinger equation;with the FFT-SI scheme, A Gaussian wave source is proposed as an efficient wave source exhibiting rapid relaxation toward the eigenstate. Our method is tested by a-one-dimensional example which has an analytical solution, and great numerical accuracy is confirmed. It is further examined by an example of time-dependent scattering and by a two-dimensional example of chaotic tunnel-scattering.