Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-03-10
J.Math.Phys. 43 (2002) 113-125
Physics
High Energy Physics
High Energy Physics - Theory
12 pages
Scientific paper
10.1063/1.1416196
The noncommutative harmonic oscillator in arbitrary dimension is examined. It is shown that the $\star$-genvalue problem can be decomposed into separate harmonic oscillator equations for each dimension. The noncommutative plane is investigated in greater detail. The constraints for rotationally symmetric solutions and the corresponding two-dimensional harmonic oscillator are solved. The angular momentum operator is derived and its $\star$-genvalue problem is shown to be equivalent to the usual eigenvalue problem. The $\star$-genvalues for the angular momentum are found to depend on the energy difference of the oscillations in each dimension. Furthermore two examples of assymetric noncommutative harmonic oscillator are analysed. The first is the noncommutative two-dimensional Landau problem and the second is the three-dimensional harmonic oscillator with symmetrically noncommuting coordinates and momenta.
Hatzinikitas Agapitos
Smyrnakis Ioannis
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