Solution of the coupled-channel schrödinger equation using constant, linear and quadratic reference potentials

Abstract

Systems of coupled second order differential equations arise in many problems in molecular quantum physics. In this paper we investigate approximate potential methods that solve these differential equations. A series method for the evaluation of the propagators is developed for the multichannel Schrodinger equation where the reference potential is expressed as a polynomial. The case of a linear approximate potential is treated in detail and the results are compared with the Magnus and Bessel methods which approximate the potential as a constant in each interval. The importance of fitting the potentials at the zeroes of a Legendre polynomial is shown. Optimum fitting of the potential results in second and fourth order global convergence respectively for constant and linear fits. Richardson extrapolation is used to increase the accuracy of the low order methods. Explicit formulae are presented for the first order perturbative corrections to the Magnus propagators. The importance of adding the leading terms ...