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arXiv · 1009.1918

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

Aaron Farrell·Brandon P. van Zyl
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Abstract

We examine the zero-range limit of the finite square well in arbitrary dimensions through a systematic analysis of the reduced, s-wave two-body time-independent Schr\"odinger equation. A natural consequence of our investigation is the requirement of a delta-function multiplied by a regularization operator to model the zero-range limit of the finite-square well when the dimensionality is greater than one. The case of two dimensions turns out to be surprisingly subtle, and needs to be treated separately from all other dimensions.

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Aaron Farrell, Brandon P. van Zyl. 2010-09-10. s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions. https://doi.org/10.1139/p10-061

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