2 research outputs found
Testing spatial noncommutativiy via the Aharonov-Bohm effect
The possibility of detecting noncommutative space relics is analyzed using
the Aharonov-Bohm effect. We show that, if space is noncommutative, the
holonomy receives non-trivial kinematical corrections that will produce a
diffraction pattern even when the magnetic flux is quantized. The scattering
problem is also formulated, and the differential cross section is calculated.
Our results can be extrapolated to high energy physics and the bound is found. If this bound holds, then noncommutative
effects could be explored in scattering experiments measuring differential
cross sections for small angles. The bound state Aharonov- Bohm effect is also
discussed.Comment: 16 pp, Revtex 4, 2 fig, new references added. To appear in PR
Non-Commutative Quantum Mechanics
A general non-commutative quantum mechanical system in a central potential
in two dimensions is considered. The spectrum is bounded from below
and for large values of the anticommutative parameter , we find an
explicit expression for the eigenvalues. In fact, any quantum mechanical system
with these characteristics is equivalent to a commutative one in such a way
that the interaction is replaced by ,
where is the hamiltonian of the two-dimensional harmonic
oscillator and is z- component of the angular momentum. For other
finite values of the model can be solved by using perturbation theory.Comment: Minors corrections and some references removed. To appear in PR