System of interacting harmonic oscillators in rotationally invariant noncommutative phase space

Highlights: • Rotationally invariant noncommutative phase space is studied. • Interacting harmonic oscillators are examined in the noncommutative phase space. • Influence of noncommutativity on the spectrum of the system is found and analyzed. - Abstract: Rotationally invariant space with noncommutativity of coordinates and noncommutativity of momenta of canonical type is considered. A system of N interacting harmonic oscillators in uniform field and a system of N particles with harmonic oscillator interaction are studied. We analyze effect of noncommutativity on the energy levels of these systems. It is found that influence of coordinates noncommutativity on the energy levels of the systems increases with increasing of the number of particles. The spectrum of N free particles in uniform field in rotationally invariant noncommutative phase space is also analyzed. It is shown that the spectrum corresponds to the spectrum of a system of N harmonic oscillators with frequency determined by the parameter of momentum noncommutativity.