Numerical and Analytical Study of the Bound States of the $-α/x^2$ Potential
The quantum mechanical bound states of the $-α/x^2$ 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.'' We present results here as a case study in undergraduate research --- two independent methodologies are used: one analytical (with very unfamiliar non-elementary functions) and one numerical (with very straightforward methodology). These play complementary roles in arriving at solutions and achieving insights in this problem.
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