System of harmonic oscillators in a rotationally-invariant noncommutative phase space

Algebra with noncommutativity of coordinates and noncommutativity of momenta which is rotationally-invariant and equivalent to noncommutative algebra of the canonical type is considered. In the framework of algebra, the effect of space quantization on the spectrum of systems of harmonic oscillators is studied. Among them, two interacting oscillators, a system of three interacting oscillators, and a harmonic oscillator chain are examined. The energy levels of the systems are found up to the second orders in the parameters of noncommutativity. We conclude that space quantization has an effect on the frequencies of the harmonic oscillators.