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We discuss a general setup which allows the study of the perturbation theoryof an arbitrary, locally harmonic 1D quantum mechanical potential as well asits multi-variable (many-body) generalization. The latter may form a prototypefor regularized quantum field theory. We first generalize the method ofBender-Wu, and derive exact recursion relations which allow the determinationof the perturbative wave-function and energy corrections to an arbitrary order,at least in principle. For 1D systems, we implement these equations in an easyto use Mathematica package we call BenderWu. Our package enables quickhome-computer computation of high orders of perturbation theory (about 100orders in 10-30 seconds, and 250 orders in 1-2h) and enables practical study ofa large class of problems in Quantum Mechanics. We have two hopes concerningthe BenderWu package. One is that due to resurgence, large amount ofnon-perturbative information, such as non-perturbative energies andwave-functions (e.g. WKB wave functions), can in principle be extracted fromthe perturbative data. We also hope that the package may be used as a teachingtool, providing an effective bridge between perturbation theory andnon-perturbative physics in textbooks. Finally, we show that for themulti-variable case, the recursion relation acquires a geometric character, andhas a structure which allows easy parallelization to computer clusters.

Aspects of Perturbation theory in Quantum Mechanics: The BenderWu Mathematica package