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We examine the zero-range limit of the finite square well in arbitrarydimensions through a systematic analysis of the reduced, s-wave two-bodytime-independent Schr\"odinger equation. A natural consequence of ourinvestigation is the requirement of a delta-function multiplied by aregularization operator to model the zero-range limit of the finite-square wellwhen the dimensionality is greater than one. The case of two dimensions turnsout to be surprisingly subtle, and needs to be treated separately from allother dimensions.

s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions