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Two-dimensional Coulomb scattering of a quantum particle: Construction of radial wave functions

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Abstract

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.

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

    V. V. Pupyshev

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  1. V. V. Pupyshev
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Correspondence to V. V. Pupyshev.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 186, No. 1, pp. 123–141, January, 2016.

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Pupyshev, V.V. Two-dimensional Coulomb scattering of a quantum particle: Construction of radial wave functions. Theor Math Phys 186, 101–117 (2016). https://doi.org/10.1134/S0040577916010098

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