Abstract
We assume that a charged quantum particle moves in a space of dimension d = 2, 3,... and is scattered by a fixed Coulomb center. We derive and study expansions of the wave function and all radial functions of such a particle in integer powers of the wave number and in Bessel functions of a real order. We prove that finite sums of such expansions are asymptotic approximations of the wave functions in the low-energy limit.
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Pupyshev, V.V. Coulomb Scattering of a Slow Quantum Particle in a Space of Arbitrary Dimension. Theor Math Phys 195, 548–556 (2018). https://doi.org/10.1134/S0040577918040062
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DOI: https://doi.org/10.1134/S0040577918040062