Scattering in Noncommutative Quantum Mechanics

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 θ → 0.

Aharonov–Casher effect for spin-1 particles in a non-commutative space

“…It is interesting to extend these results to higher order terms, however it seems that obtaining an exact result similar to the commutative case is not possible by these methods. For some other interesting relevant papers see [27][28][29][30][31][32][33][34].…”

Bound state energies and phase shifts of a non-commutative well

“…Although scattering has been studied rather extensively in the context of non-commutative quantum field theories [4,23], much less has been done on potential scattering in non-commutative quantum mechanics in either two or three dimensions [24][25][26]. These few studies depart from a leading order expansion in the non-commutative parameter of either the Moyal product or Bopp-shifted formulation of the Schrödinger equation.…”

Scattering problem in deformed space with minimal length

“…At the same time as far as we know there were no papers on the investigation of the quantum-mechanical scattering problem in deformed space with minimal length described by algebra (1). There are only a few papers where scattering problem on the noncommutative space with canonical deformation [Xi, Xj ] = iθij was considered [20,21,22].…”