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.
@article{TMF_2014_180_3_a4,
author = {V. V. Pupyshev},
title = {The~length and effective radius of two-dimensional scattering of a~quantum particle by a~centrally symmetric short-range potential},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {342--367},
publisher = {mathdoc},
volume = {180},
number = {3},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a4/}
}
TY - JOUR AU - V. V. Pupyshev TI - The~length and effective radius of two-dimensional scattering of a~quantum particle by a~centrally symmetric short-range potential JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2014 SP - 342 EP - 367 VL - 180 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a4/ LA - ru ID - TMF_2014_180_3_a4 ER -
%0 Journal Article %A V. V. Pupyshev %T The~length and effective radius of two-dimensional scattering of a~quantum particle by a~centrally symmetric short-range potential %J Teoretičeskaâ i matematičeskaâ fizika %D 2014 %P 342-367 %V 180 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2014_180_3_a4/ %G ru %F TMF_2014_180_3_a4
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/