coulomb scattering in non-commutative quantum mechanics

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ID: 164003
2013
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Abstract
Recently we formulated the Coulomb problem in a rotationally invariant NC configuration space specified by NC coordinates xi, i = 1, 2, 3, satisfying commutation relations [xi, xj ] = 2iλεijkxk (λ being our NC parameter). We found that the problem is exactly solvable: first we gave an exact simple formula for the energies of the negative bound states Eλn < 0 (n being the principal quantum number), and later we found the full solution of the NC Coulomb problem. In this paper we present an exact calculation of the NC Coulomb scattering matrix Sλj (E) in the j-th partial wave. As the calculations are exact, we can recognize remarkable non-perturbative aspects of the model: 1) energy cut-off — the scattering is restricted to the energy interval 0 < E < Ecrit = 2/λ2; 2) the presence of two sets of poles of the S-matrix in the complex energy plane — as expected, the poles at negative energy EIλn = Eλn for the Coulomb attractive potential, and the poles at ultra-high energies EIIλn = Ecrit − Eλn for the Coulomb repulsive potential. The poles at ultra-high energies disappear in the commutative limit λ→0.
Reference Key
glikov2013actacoulomb Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Veronika Gáliková;Peter Prešnajder
Journal the journal of nutrition
Year 2013
DOI
10.14311/AP.2013.53.0427
URL
https://ojs.cvut.cz/ojs/index.php/ap/article/view/1852
Keywords
engineering (general) civil engineering (general)

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