Symbolic computation in physics and chemistry: Applications of the inner projection technique and of a new summation method for divergent series

Abstract

The goal of this article is to illustrate the use of symbolic computation in solving problems in physics and chemistry. For instance, the application of the inner projection technique combined with renormalization is shown to give very tight bounds for the ground-state energy of anharmonic oscillators. Some typical results are presented. Further, it has been observed that inner projection is directly applicable to the PPP and Hubbard Hamiltonians. The results for the model of benzene are briefly presented. A new method for summing divergent series, which we call the Weniger summation method, is proposed. This method is used, with excellent results, for the summation of divergent perturbation series for the energy of anharmonic oscillators. This method is also applied for the summation of the divergent series corresponding to the ground-state energy of the Hubbard Hamiltonian of the infinite chain. Other applications of the Weniger summation method to diffusion and heat conduction problems are summarized.