It is demonstrated that it is possible to solve the time-dependent Schroedinger equation in 10d by discarding unimportant product basis functions. The matrix-vector products required to propagate an initial wave packet are done at a cost that scales as n(D+1) where n is a representative number of 1D basis functions and D is the dimensionality. Discarding unimportant basis functions drastically reduces the size of the vectors that must be stored. With D 20 and n 16 only similar to 26GB is required to store the wavefunction. The ideas are applied to a model Hamiltonian for hydrocarbon chains. (C) 2010 Elsevier B.V. All rights reserved.