Espalhamento quântico não relativístico no espaço tempo de uma corda cósmica

Abstract

In this work, we investigate non-relativistic quantum scattering by a Coulomb potential in the spacetime of a cosmic string. Initially, we review the fundamentals of non-relativistic quantum mechanics, with emphasis on the Schrödinger equation and its essential properties. Then, we develop the theory of quantum scattering, specifying the formalism for the Coulomb potential. The cosmic string is described by the line element ds² = −dt² +dr² +r²dθ² +α²r²sin²θdφ², for which we formulate the Schrödinger equation and explicitly solve the problem for the scattering states. From these solutions, we determine the phase shift, the scattering amplitude, and the cross-section, highlighting the modifications introduced by the topological defect.Furthermore, we show that the energy spectrum of the bound states can be obtained from the poles of the scattering matrix, resulting in energy levels corrected by the geometric parameter α. The results obtained reveal that the topology associated with the cosmic string directly influences quantum observables, manifesting itself both in the asymptotic behavior of the scattered waves and in the geometric splitting of the hydrogen atom's energy levels.