Parabolic coordinates allow Schrödinger’s equation to be solved analytically for a particle confined to the xy plane and incident with velocity v on a potential C/r. In sharp contrast to the three‐dimensional case, the cross section assumes its classical value only in the rationally foreseeable classical regime ‖C‖/ℏv≫1, but not otherwise; and in this low‐velocity regime the enhancement factor (probability density at the origin) for an attractive potential tends to 2 (independently of the value of ‖C‖), instead of diverging as in three dimensions like some inverse power of v.
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Papers| May 01 1983
Rutherford scattering in two dimensions
G. Barton; Rutherford scattering in two dimensions. Am. J. Phys. 1 May 1983; 51 (5): 420–422. https://doi.org/10.1119/1.13228
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