Geodesic
Two-dimensional Coulomb scattering of a~quantum particle: Construction of radial wave functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 1, pp. 123-141

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We prove that radial wave functions of a charged quantum particle moving in a two-dimensional plane of the three-dimensional coordinate space and scattering by a Coulomb center at rest in the same plane are governed by the Coulomb equation with a half-integer index. We investigate the structure of these functions and consider three physically interesting limits: the non-Coulomb limit and high- and low-energy limits. We explicate the basic differences between two- and three-dimensional Coulomb scattering.
Keywords: two-dimensional Coulomb scattering, radial function, zero-energy limit. 
@article{TMF_2016_186_1_a7,
     author = {V. V. Pupyshev},
     title = {Two-dimensional {Coulomb} scattering of a~quantum particle: {Construction} of radial wave functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {123--141},
     publisher = {mathdoc},
     volume = {186},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_1_a7/}
}
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V. V. Pupyshev. Two-dimensional Coulomb scattering of a~quantum particle: Construction of radial wave functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 1, pp. 123-141. http://geodesic.mathdoc.fr/item/TMF_2016_186_1_a7/