s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions
Quantum Physics
2015-05-19 v1 Quantum Gases
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.
Keywords
Cite
@article{arxiv.1009.1918,
title = {s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions},
author = {Aaron Farrell and Brandon P. van Zyl},
journal= {arXiv preprint arXiv:1009.1918},
year = {2015}
}