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arXiv · 1008.5002

Short-range interaction in three-dimensional quantum mechanics

Taksu Cheon
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Abstract

We show that it is possible to define shape-independent three-dimensional short-range quantum interactions in two parameter form for non-spherical angular momentum channels through double rescaling of potential strength. Unlike the special case of $l=0$, where the zero range limit of the system is renormalizable, the effective ranges diverge for $l /ne 0$ channels, and the system becomes trivial at zero-size limit. It is also shown that the two-parameter representation with finite interaction range is useful in analyzing phase shifts with accuracy and describing resonances in non-spherical scatterings.

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Taksu Cheon. 2010-08-30. Short-range interaction in three-dimensional quantum mechanics. https://doi.org/10.1016/j.physleta.2010.09.040

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