PERTURBATIVE SOLUTIONS OF QUANTUM MECHANICAL PROBLEMS BY SYMBOLIC COMPUTATION: A REVIEW

It is shown that Symbolic Computation provides excellent tools for solving quantum mechanical problems by perturbation theory. The method presented herein solves for both the eigenfunctions and eigenenergies as power series in the order parameter where each coefficient of the perturbation series is obtained in closed form. The algorithms are expressed in the Maple symbolic computation system but can be implemented on other systems. This approach avoids the use of an infinite basis set and some of the complications of degenerate perturbation theory. It is general and can, in principle, be applied to many separable systems.