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

Understand

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.