A systematic determination of higher-order exponential (Magnus) scattering propagators

An algebraic method for determining Magnus propagators of arbitrary order is described. These propagators preserve the wronskian and therefore the linear independence of the solutions and can be used for numerical solutions of multichannel time-dependent and time-independent Schrödinger equations. As an example the propagator for the single-channel Schrödinger equation is derived analytically for quadratic reference potentials up to seventh order in the stepsize. Recent results obtained by purely numerical procedures are verified, corrected, improved and considerably extended.