Variational principle for an improved basis set for the description of scattering processes

We discuss the choice of the basis set to calculate excitations in time-dependent problems. Starting from a variational principle which minimizes the time-integrated coupling strength out of a given initial state, an equation determining the ''optimal'' basis is derived. We discuss the application of this concept to the harmonic oscillator of variable frequency and to electronic excitations in heavy-ion collisions. We also comment on particle production in time-dependent gravitational fields