A method for the rapid calculation of matrix elements with highly oscillatory JWKB radial wavefunctions

A method for the rapid computation of matrix elements with JWKB radial wavefunctions is discussed. The method consists of dividing the range of integration into segments determined by the nodes of the semiclassical wavefunction. The desired matrix elements are calculated by summing the contributions from each segment which are evaluated by integrating between nodes with a Gauss-Mehler quadrature formula. The results are compared with exact quantum mechanical calculations and were found to agree within 1–2%. The calculations with the present method were generally five to ten times faster than the quantum mechanical calculations.