Representation of noncommutative phase space

Abstract

The representations of the algebra of coordinates and momenta of noncommutative phase space are given. We study, as an example, the harmonic oscillator in noncommutative space of any dimension. Finally the map of Sch$\ddot{o}$dinger equation from noncommutative space to commutative space is obtained.

Latex file, 10 pages

References in corpus (7)

• Noncommutative Field Theory
• Noncommutative Quantum Mechanics from Noncommutative Quantum Field Theory
• Two phases of the noncommutative quantum mechanics
• Fractional Angular Momentum in Noncommutative Space
• Quantum Mechanics on the Noncommutative Torus
• Noncommutative Quantum Mechanics: The Two-Dimensional Central Field
• The noncommutative harmonic oscillator in more than one dimensions

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• Landau Problem in Noncommutative Quantum Mechanics
• Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
• Weak equivalence principle in noncommutative phase space and the parameters of noncommutativity
• Probing noncommutative theories with quantum optical experiments
• Exact solution of two dimensional Dunkl harmonic oscillator in Non-Commutative phase-space
• On the Landau system in noncommutative phase-space
• Non-Relativistic Holography -- A Group-Theoretical Perspective
• The Aharonov-Casher effect for spin-1 particles in non-commutative quantum mechanics
• Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity
• Entropy and Information of a harmonic oscillator in a time-varying electric field in 2D and 3D noncommutative spaces
• Commutator Anomaly in Noncommutative Quantum Mechanics
• Induced entanglement entropy of harmonic oscillators in noncommutative phase space
• The He-McKellar-Wilkens effect for spin one particles in non-commutative quantum mechanics
• Bohr-van Leeuwen theorem in non-commutative space
• Connes spectral distance and nonlocality of generalized noncommutative phase spaces
• Two-dimensional Noncommutative atom Gas with Anandan interaction
• Higher Order Theories and its Relationship with Noncommutativity
• ${\pi }^{+}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{-}$ colliding in noncommutative space
• Thermal Properties of Gauge-Invariant Graphene in Noncommutative Phase-Space
• Improved quark coalescence model for spin alignments of vector mesons