Solving the time-dependent Schroedinger equation by discarding high-energy basis functions

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 ∼26 GB is required to store the wavefunction. The ideas are applied to a model Hamiltonian for hydrocarbon chains.