A quadrature scheme for matrix elements between numerical wavefunctions (Q1064008)

A Gaussian-like quadrature scheme for evaluating matrix elements between one-dimensional numerical wavefunctions is developed. The abscissae are the zeroes of a high vibrational wavefunction for the potential curve concerned, and the weights are defined so that integrals over low-order wavefunctions are evaluated exactly. The method gives results sufficiently accurate for most purposes with only a few quadrature points, and is significantly more accurate than Gauss-Hermite quadrature. It should be particularly valuable in reactive and inelastic scattering problems.