PERTURBATIVE SOLUTIONS OF QUANTUM-MECHANICAL PROBLEMS BY SYMBOLIC COMPUTATION

Symbolic computation provides excellent tools for solving quantum mechanical problems by perturbation theory. The techniques presented herein avoid the use of an infinite basis set and some of the complications of degenerate perturbation theory. The algorithms are expressed in the Maple symbolic computation system and solve for both the eigenfunctions and eigenenergies as power series in the order parameter. Further, each coefficient of the perturbation series is obtained in closed form. In particular, this paper examines the application of these techniques to R. A. Moore's method for solving the radial Dirac equation. One is confident that the techniques presented will also be useful in other applications. © 1990.