NEGATIVE IMAGINARY POTENTIALS IN TIME-DEPENDENT QUANTUM MOLECULAR-SCATTERING

Reflection or wrap around of the wavefunction from the grid edges is o ften avoided in time-dependent quantum mechanical calculations by usin g a negative imaginary potential (NIP) near the grid edges. The stabil ity of the various (second-order differencing, split operator, Chebysh ev polynomial and short iterative Lanczos) schemes used, in conjunctio n with the NIP, for time evolution is discussed using collinear (He, H -2(+)) collisions as a test case. It is shown that the difficulties en countered in obtaining converged reaction probability [P-R(E)] values at high energies for the system when NIPs are used, are avoided by usi ng a properly chosen damping function externally.