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