Application of symplectic integrator to stationary reactive-scattering problems: Inhomogeneous Schrödinger equation approach

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.