Geodesic
Two-dimensional Coulomb scattering of a~quantum particle: Wave functions and Green's functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 252-271

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We solve the problem of the propagation of a charged quantum particle in a two-dimensional plane embedded in the three-dimensional coordinate space. We consider scattering of this particle by a stable Coulomb center situated in the same plane. We study the wave function of this particle, its Green's function, and all radial components of these functions. We derive uniform majorant bounds on absolute values of these functions and find the wave function representation in terms of regular radial Coulomb functions and the scattering amplitude representation via partial phases. We obtain integral representations of the Greens's function and all its radial components.
Keywords: two-dimensional scattering, Coulomb wave function, Coulomb Green's function. 
@article{TMF_2016_186_2_a5,
     author = {V. V. Pupyshev},
     title = {Two-dimensional {Coulomb} scattering of a~quantum particle: {Wave} functions and {Green's} functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {252--271},
     publisher = {mathdoc},
     volume = {186},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a5/}
}
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V. V. Pupyshev. Two-dimensional Coulomb scattering of a~quantum particle: Wave functions and Green's functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 252-271. http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a5/