Noncommutative 3D harmonic oscillator
Copyright policy )Noncommutative 3D harmonic oscillator
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
- University of Trieste Italy
High Energy Physics - Theory, High Energy Physics - Theory (hep-th), Algebraic methods, Noncommutative geometry, Noncommutative geometry in quantum theory, FOS: Physical sciences, Solutions of wave equations: bound states; Noncommutative geometry; Algebraic methods, Solutions of wave equations: bound state, Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
High Energy Physics - Theory, High Energy Physics - Theory (hep-th), Algebraic methods, Noncommutative geometry, Noncommutative geometry in quantum theory, FOS: Physical sciences, Solutions of wave equations: bound states; Noncommutative geometry; Algebraic methods, Solutions of wave equations: bound state, Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
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