Entangled state representations in non-commutative space and their applications
Sicong Jing, Qiuyu Liu, Hong-Yi Fan
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called entangled state representations. Furthermore, we derive unitary transformations between the new representations and the ordinary one used in noncommutative quantum mechanics (NCQM) and obtain eigenfunctions of some basic operators in these representations. To show the potential applications of the entangled state representations, a two-dimensional harmonic oscillator on the noncommutative plane with both coordinate-coordinate and momentum-momentum couplings is exactly solved.
arXiv:hep-th/0503233•Journal of Physics A Mathematical and General•Sep 14, 2005•10 citations