Noncommutative 3D harmonic oscillator

Abstract

We find transformation matrices allowing to express non-commutative three dimensional harmonic oscillator in terms of an isotropic commutative oscillator, following ``philosophy of simplicity'' approach. Non-commutative parameters have physical interpretation in terms of an external magnetic field. Furthermore, we show that for a particular choice of noncommutative parameters there is an equivalent anisotropic representation, whose transformation matrices are far more complicated. We indicate a way to obtain the more complex solutions from the simple ones.

7pages, LateX 2e, no figures; in print on J.Phys.A

References in corpus (6)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• The Landau problem and noncommutative quantum mechanics
• Two phases of the noncommutative quantum mechanics
• Isotropic representation of noncommutative 2D harmonic oscillator
• Orbital Magnetism of Two-Dimension Noncommutative Confined System

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