Entangled state representations in noncommutative quantum mechanics

Abstract

We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called entangled state representations. Furthermore, we derive unitary transformations between the new representations and the ordinary one used in noncommutative quantum mechanics (NCQM) and obtain eigenfunctions of some basic operators in these representations. To show the potential applications of the entangled state representations, a two-dimensional harmonic oscillator on the noncommutative plane with both coordinate-coordinate and momentum-momentum couplings is exactly solved.

References in corpus (15)

• String Theory and Noncommutative Geometry
• Quantifying Entanglement
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Feasible Entanglement Purification for Quantum Communication
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• D-branes and the Noncommutative Torus
• Non-Commutative Quantum Mechanics
• Quantum mechanics on the noncommutative plane and sphere
• Aharonov-Bohm Effect in Noncommutative Spaces
• Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects
• Isotropic representation of noncommutative 2D harmonic oscillator
• Non-commutative Oscillators and the commutative limit
• The noncommutative harmonic oscillator in more than one dimensions
• Orbital Magnetism of Two-Dimension Noncommutative Confined System
• Dual D-Brane Actions on $Ad{S}^5\times S^5$

Cited by in corpus (1)

• Noncommutative geometry induced by spin effects