Numerical grid methods for quantum-mechanical scattering problems

Abstract

We show how the finite-element method can be implemented using a discrete variable representation to provide an efficient means for directly solving the time-independent Schr\"odinger equation on a multidimensional numerical grid. For collision problems, an exterior complex scaling transformation obviates the need for explicit imposition of asymptotic boundary conditions, making the method particularly useful for studying three-body breakup. The method is illustrated by studying an analytically solvable two-dimensional (2D) breakup problem as well as a 2D model problem with exponential potentials.