One step time propagation method for systems with time-dependent Hamiltonians

A one step time propagation method for systems with time-dependent Hamiltonians is proposed. ?The essential feature of the method is the use of a smallest grid with only two points to represent the physical time coordinate. The method is in principle the most efficient possible among those based on an extended Hilbert space formalism. The efficiency is gained in sacrificing unphysical information contained in the vectors of an extended Hilbert space. The method is implemented and tested using an one-dimensional model system. The Chebyshev implementation of the method is found of capable of longer than 10 ns time propagation.