Multiresolution of the one dimensional free-particle propagator

Abstract Novel methods to integrate the time-dependent Schrödinger equation within the framework of multiscale approximation is presented. The methods are based on symplectic splitting algorithms to separate the kinetic and potential parts of the corresponding propagator. The semigroup associated with the free-particle Schrödinger operator is represented in a multiwavelet basis. The propagator is effectively discretized with a contour deformation technique, which overcomes the challenges presented by previous discretization methods. The discretized operator is then employed in simple numerical simulations to test the validity of the implementation and to benchmark its precision.