A new kind of representations on noncommutative phase space

Details A new kind of representations on noncommutative phase space A new kind of representations on noncommutative phase space

2009-02-22

arxiv.org/abs/0902.3782v1

Phys.Lett.A372:7109-7116,2008

Physics

Mathematical Physics

Scientific paper

10.1016/j.physleta.2008.10.052

We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties between degrees of freedom of different coordinate and momentum components. To show their potential applications, we derive explicit expressions of Wigner function and Wigner operator in the new representations, as well as solve exactly a two-dimensional harmonic oscillator on the noncommutative phase plane with both kinetic coupling and elastic coupling.

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