We review the development of the time-dependent close-coupling method to study atomic and molecular few body dynamics. Applications include electron and photon collisions with atoms, molecules, and their ions.

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A test of the lattice, time-dependent Schrödinger equation (LTDSE) method for treating inelastic ion–atom collisions is performed by treating state-selective charge transfer in 10–1000 keV/u Be4+ + H collisions. This system possesses a greater charge asymmetry of the colliding nuclei than has been treated in previous applications of the method. Consequently, its ability to represent well the dynamical evolution of the electronic wavefunction within the combination of a shallow and a deep potential well with a single coordinate- and momentum-space discretization is tested. New results are also computed using other, standard approaches, the atomic-orbital close-coupling and classical trajectory Monte Carlo methods, to provide comparisons with the LTDSE results owing to their well-established regimes of applicability and behaviours.

The doorway-window representation of sequential pump-probe spectroscopy, derived by solving the nonlinear exciton equations, is used to study exciton dynamics in molecular aggregates. Exciton relaxation is incorporated through a multilevel Redfield relaxation superoperator calculated using the Brownian oscillator spectral density for the collective phonon coordinates. Optical pulses are included using a mixed time and frequency domain (Wigner spectrogram) representation. Numerical results are presented for a five-chromophore model aggregate.