Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space

Abstract

We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that for a specific choice of the noncommutative parameters, the time reversal symmetry of the systems get restored since the energy spectrum becomes degenerate. This is in contrast to the noncommutative configuration space where the time reversal symmetry of the harmonic oscillator is always broken.

7 pages Latex

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Cited by in corpus (23)

• Weak equivalence principle in noncommutative phase space and the parameters of noncommutativity
• Probing noncommutative theories with quantum optical experiments
• Emergence of Geometric phase shift in Planar Non-commutative Quantum Mechanics
• Effect of noncommutativity on the spectrum of free particle and harmonic oscillator in rotationally invariant noncommutative phase space
• Response of simple quantum systems to different polarizations of gravitational waves in noncommutative phase-space
• Semiclassical and quantum description of motion on noncommutative plane
• Kinematic variables in noncommutative phase space and parameters of noncommutativity
• Pauli Oscillator In Noncommutative Space
• Emergent entropy of exotic oscillators and squeezing in three-wave mixing process
• Variations on the Planar Landau Problem: Canonical Transformations, A Purely Linear Potential and the Half-Plane
• System of interacting harmonic oscillators in rotationally invariant noncommutative phase space
• Features of free particles system motion in noncommutative phase space
• Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states
• Noncommutative Complex Scalar Field and Casimir Effect
• Time reversal and rotational symmetries in noncommutative phase space
• Influence of noncommutativity on the motion of Sun-Earth-Moon system and the weak equivalence principle
• Trace of phase-space noncommutativity in the response of a free particle to linearized gravitational waves
• Some Biorthogonal Families of Polynomials Arising in Noncommutative Quantum Mechanics
• The quantum and Klein-Gordon oscillators in a non-commutative complex space and the thermodynamic functions
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
• Features of description of composite system's motion in twist-deformed space-time
• Harmonic oscillator chain in noncommutative phase space with rotational symmetry
• Exact continuity equation in a space with minimal length