On The Use Of The Symbolic Language Maple In Physics And Chemistry: Several Examples

The purpose of this paper is to present several physical and chemical applications of the symbolic computation language Maple which has been developed by the Symbolic Computation Group at the University of Waterloo. The paper will highlight the activity of the Quantum Theory Group of the Department of Applied Mathematics at the University of Waterloo during the years 1985–1992, which has already led to more than 20 articles on applications of Maple. Special attention will be given to examples from quantum mechanics and quantum chemistry: the application of the inner projection technique to anharmonic oscillators yielding explicit expressions for Löwdin's approximants as well as to simple many-electron problem, the use of hypervirial and Hellmann-Feynman theorems for the computation of perturbation series coefficients in rational arithmetics, the creation of coupled-cluster equations by the computer, the use of several techniques including the method of Weniger for the summation of divergent series as they occur in perturbation expansions for anharmonic oscillators or in heat conduction with nonlinear boundary conditions. In all these examples, the symbolic computation language Maple proved to be very useful, and in many cases, it was actually indispensable for obtaining a solution or for keeping control of the accuracy.