An application of interpolating scaling functions to wave packet propagation

Abstract

Wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an equidistantly spaced grid. They have compact support of the size determined by the underlying interpolating polynomial that is used to generate ISF. In this basis the potential energy matrix is diagonal and the kinetic energy matrix is sparse and, in the 1D case, has a band-diagonal structure. An important feature of the basis is that matrix elements of a Hamiltonian are exactly computed by means of simple algebraic transformations efficiently implemented numerically. Therefore the number of grid points and the order of the underlying interpolating polynomial can easily be varied allowing one to approach the accuracy of pseudospectral methods in a regular manner, similar to high order finite difference methods. The results of numerical simulations of an H+H_2 collinear collision show that the ISF provide one with an accurate and efficient representation for use in the wave packet propagation method.