Short-range interaction in three-dimensional quantum mechanics

Details Short-range interaction in three-dimensional quantum mechanics Short-range interaction in three-dimensional quantum mechanics

2010-08-30

arxiv.org/abs/1008.5002v1

Phys.Lett.A374:4585-4588,2010

Physics

Quantum Physics

LaTeX 7 pages, 3 figures, Elsevier format

Scientific paper

10.1016/j.physleta.2010.09.040

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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