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 Schrödinger 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.
- Publication:
-
Physical Review A
- Pub Date:
- September 2000
- DOI:
- Bibcode:
- 2000PhRvA..62c2706R
- Keywords:
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- 34.80.Dp;
- 03.65.Nk;
- Atomic excitation and ionization by electron impact;
- Scattering theory