Systems of free particles and harmonic oscillators in rotationally-invariant noncommutative phase space

In this paper, we introduce a rotationally-invariant noncommutative algebra that is equivalent to the canonical type. This algebra is built by extending the noncommutativity parameters to tensors. These tensors are defined with the help of additional coordinates and momenta corresponding to a rotationally-invariant system. In the frame of the rotationally-invariant noncommutative algebra we investigate a system of free particles, and systems of harmonic oscillators. The energy levels of these systems are found in noncommutative phase spave with preserved rotational symmetry.