An accurate and efficient scheme for propagating the time dependent Schrödinger equation

A new propagation scheme for the time dependent Schrödinger equation is based on a Chebychev polynomial expansion of the evolution operator Û=exp(−iĤt). Combined with the Fourier method for calculating the Hamiltonian operation the scheme is not only extremely accurate but is up to six times more efficient than the presently used second order differencing propagation scheme.