Particular and homogeneous solutions of time-independent wavepacket Schrodinger equations: calculations using a subset of eigenstates of undamped or damped Hamiltonians

A variety of causal, particular and homogeneous solutions to the time-indep endent wavepacket Schrodinger equation have been considered as the basis fo r calculations using Chebychev expansions, finite-tau expansions obtained f rom a partial Fourier transform of the time-dependent Schrodinger equation, and the distributed approximating functional (DAF) representation for the spectral density operator (SDO). All the approximations are made computatio nally robust and reliable by damping the discrete Hamiltonian matrix along the edges of the finite grid to facilitate the use of compact grids. The ap proximations are found to be completely well behaved at all values of the ( continuous) scattering energy. It is found that the DAF-SDO provides a suit able alternative to Chebychev propagation.