Espalhamento quântico não relativístico no espaço tempo de uma corda cósmica

Abstract

In this work, we investigate nonrelativistic quantum scattering by a Coulomb potential in the spacetime of a cosmic string. We begin by reviewing the foundations of nonrelativistic quantum mechanics, with emphasis on the Schr¨odinger equation and its essential properties. We then develop the theory of quantum scattering, specializing the formalism to the Coulomb potential. The cosmic string is described by the line element ds2 = −dt2 +dr2 +r2dθ2 +α2r2sin2θdφ2, within which we formulate the Schr¨odinger equation and explicitly solve the problem for scat tering states. From these solutions, we determine the phase shift, the scattering amplitude, and the cross section, highlighting the modifications introduced by the topological defect. Mo reover, we show that the energy spectrum of bound states can be obtained from the poles of the scattering matrix, yielding energy levels corrected by the geometric parameter α. The results 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 energy levels of the hydrogen atom.