Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space

Abstract

We consider rotationally invariant noncommutative algebra with tensors of noncommutativity constructed with the help of additional coordinates and momenta. The algebra is equivalent to well known noncommutative algebra of canonical type. In the noncommutative phase space with rotational symmetry influence of noncommutativity on the spectrum of free particle and spectrum of harmonic oscillator is studied up to the second order in the parameters of noncommutativity. We find that because of momentum noncommutativity the spectrum of free particle is discrete and corresponds to the spectrum of harmonic oscillator in the ordinary space (space with commutative coordinates and commutative momenta). We obtain the spectrum of the harmonic oscillator in the rotationally invariant noncommutative phase space and conclude that noncommutativity of coordinates affects on its mass. The frequency of the oscillator is affected by the coordinate noncommutativity and the momentum noncommutativity. On the basis of the results, the eigenvalues of squared length operator are found and restrictions on the value of length in noncommutative phase space with rotational symmetry are analyzed.

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Cited by in corpus (7)

• Emergence of Geometric phase shift in Planar Non-commutative Quantum Mechanics
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
• Induced entanglement entropy of harmonic oscillators in noncommutative phase space
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
• Connes spectral distance and nonlocality of generalized noncommutative phase spaces
• Harmonic oscillator chain in noncommutative phase space with rotational symmetry
• Deformation quantization for systems with second-class constraints in deformed fermionic phase space