COULOMB SCATTERING IN NON-COMMUTATIVE QUANTUM MECHANICS

Authors

  • Veronika Gáliková Faculty of Mathematics, Physics and Informatics, Comenius University of Bratislava, Mlynská dolina F2, Bratislava
  • Peter Prešnajder Faculty of Mathematics, Physics and Informatics, Comenius University of Bratislava, Mlynská dolina F2, Bratislava

DOI:

https://doi.org/10.14311/AP.2013.53.0427

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 = EcritEλn for the Coulomb repulsive potential. The poles at ultra-high energies disappear in the commutative limit λ→0.

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Published

2013-10-24

How to Cite

Gáliková, V., & Prešnajder, P. (2013). COULOMB SCATTERING IN NON-COMMUTATIVE QUANTUM MECHANICS. Acta Polytechnica, 53(5), 427–432. https://doi.org/10.14311/AP.2013.53.0427

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