Geodesic
The length and effective radius of two-dimensional scattering of a quantum particle by a centrally symmetric short-range potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 3, pp. 342-367

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We derive and qualitatively analyze nonlinear and linear equations for the scattering length and effective radius. We find and investigate exact solutions of these equations in the case of a centrally symmetric rectangular potential and elucidate a relation between the effective radius and the scattering length. We are especially interested in the cases of zero and unbounded scattering lengths.
Keywords: two-dimensional scattering, short-range potential, scattering length, effective radius. 
V. V. Pupyshev. The length and effective radius of two-dimensional scattering of a quantum particle by a centrally symmetric short-range potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 3, pp. 342-367. http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a4/
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