Bound state energies and phase shifts of a non-commutative well
Non-commutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on non-commutative configuration space. Within this framework, an unambiguous definition can be given for the non-commutative well. Using this approach, we compute the bound state energies, phase shifts and scattering cross-sections of the non-commutative well. As expected, the results are very close to the commutative results when the well is large or the non-commutative parameter is small. However, the convergence is not uniform, and phase shifts at certain energies exhibit a much stronger than expected dependence on the non-commutative parameter even at small values. © 2009 IOP Publishing Ltd.