Scattering in Noncommutative Quantum Mechanics

TL;DR

This paper investigates how noncommutative space affects quantum scattering, deriving corrections to the Born approximation, analyzing unitarity and the optical theorem, and studying Gaussian potentials in noncommutative quantum mechanics.

Contribution

It provides explicit calculations of scattering corrections due to noncommutativity and demonstrates that unitarity and the optical theorem remain valid in noncommutative spaces.

Findings

Noncommutativity introduces angle-dependent corrections to scattering.

Unitarity of elastic scattering is preserved in noncommutative spaces.

Noncommutativity does not alter the optical theorem.

Abstract

We derive the correction due to noncommutativity of space on Born approximation, then the correction for the case of Yukawa potential is explicitly calculated. The correction depends on the angle of scattering. Using partial wave method it is shown that the conservation of the number of particles in elastic scattering is also valid in noncommutative spaces which means that the unitarity relation is held in noncommutative spaces. We also show that the noncommutativity of space has no effect on the optical theorem. Finally we study Gaussian function potential in noncommutative spaces which generates delta function potential as $\theta \to 0$.