Magnetic fields in noncommutative quantum mechanics

Dedicated to the memory of Julius Wess. Work presented by F. Gieres at the conference "Non-commutative Geometry and Physics" (Orsay, April 2007)International audienceWe discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between various approaches and results that are scattered in the literature