Scattering by a contact potential in three and lower dimensions

Details Scattering by a contact potential in three and lower dimensions Scattering by a contact potential in three and lower dimensions

2001-03-04

arxiv.org/abs/quant-ph/0103013v1

J. Phys. A 34 (2001) 1911-1918

Physics

Quantum Physics

REVTeX, 9 pages, no figure

Scientific paper

10.1088/0305-4470/34/9/308

We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is surprising that it gives a nonvanishing cross section when $\alpha=1$ and $\Omega=-1$. When the contact potential is approached by a spherical square well potential instead of the above spherical shell one, one obtains basically the same result except that the parameter $\Omega$ that gives a nonvanishing cross section is different. Similar problems in two and one dimensions are studied and results of the same nature are obtained.

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