The quantum mechanical bound states of the −α/x2 potential are truly anomalous. We revisit this problem by adopting a slightly modified version of this potential, one that adopts a cutoff in the potential arbitrarily close to the origin. The resulting solutions are completely well-defined and “normal,” and provide us with additional insight into the solutions of the “bare” −α/x2 potential. We present results here as a case study in undergraduate research—two independent methodologies are used: one analytical (albeit with very unfamiliar non-elementary functions) and one numerical (with a very straightforward methodology). These play complementary roles in arriving at solutions and achieving insights into this problem.
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