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

Abstract.

A variety of causal, particular and homogeneous solutions to the time-independent wavepacket Schrödinger equation have been considered as the basis for calculations using Chebychev expansions, finite-τ expansions obtained from a partial Fourier transform of the time-dependent Schrödinger equation, and the distributed approximating functional (DAF) representation for the spectral density operator (SDO). All the approximations are made computationally robust and reliable by damping the discrete Hamiltonian matrix along the edges of the finite grid to facilitate the use of compact grids. The approximations are found to be completely well behaved at all values of the (continuous) scattering energy. It is found that the DAF–SDO provides a suitable alternative to Chebychev propagation.