Two-dimensional motion of a~slow quantum particle in the~field of a~central long-range potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 3, pp. 405-428
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We study the two-dimensional motion of a slow quantum particle in the field of a central long-range potential decaying in the limit of long distances $r$ as the power $r^{-\beta}$ with the exponent $\beta\in(1,2)$. We find the low-temperature asymptotic behavior for all partial phases and the differential cross section of the particle scattering and derive a rather simple approximation for the weakly bound state energy.
Keywords:
two-dimensional scattering, central long-range potential, low-energy asymptotics, weakly bound state energy.
@article{TMF_2019_199_3_a4,
author = {V. V. Pupyshev},
title = {Two-dimensional motion of a~slow quantum particle in the~field of a~central long-range potential},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {405--428},
publisher = {mathdoc},
volume = {199},
number = {3},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2019_199_3_a4/}
}
TY - JOUR AU - V. V. Pupyshev TI - Two-dimensional motion of a~slow quantum particle in the~field of a~central long-range potential JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2019 SP - 405 EP - 428 VL - 199 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2019_199_3_a4/ LA - ru ID - TMF_2019_199_3_a4 ER -
%0 Journal Article %A V. V. Pupyshev %T Two-dimensional motion of a~slow quantum particle in the~field of a~central long-range potential %J Teoretičeskaâ i matematičeskaâ fizika %D 2019 %P 405-428 %V 199 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2019_199_3_a4/ %G ru %F TMF_2019_199_3_a4
V. V. Pupyshev. Two-dimensional motion of a~slow quantum particle in the~field of a~central long-range potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 3, pp. 405-428. http://geodesic.mathdoc.fr/item/TMF_2019_199_3_a4/