Noncommutative quantum mechanics
Abstract
We discuss the main features of noncommutative quantum mechanics, a version of nonrelativistic quantum mechanics that involves noncommuting coordinates. After finding a representation for the algebra obeyed by the coordinates and momenta, we analyze the changes due to the noncommutative nature of the coordinates. The noncommutative twodimensional harmonic oscillator is discussed in detail. Under certain restrictions, the effect of the noncommutativity is found to be equivalent to a Landau interaction. The modifications produced by the noncommutativity on the thermodynamic functions of the oscillator also are studied.
 Publication:

American Journal of Physics
 Pub Date:
 May 2004
 DOI:
 10.1119/1.1624116
 arXiv:
 arXiv:hepth/0301237
 Bibcode:
 2004AmJPh..72..608G
 Keywords:

 01.50.i;
 03.65.Ge;
 Educational aids;
 Solutions of wave equations: bound states;
 High Energy Physics  Theory
 EPrint:
 45 pages, 11 figures, lectures delivered at the XII Jorge Andre Swieca Summar School, Section Particles and Fields, Campos de Jordao, Brazil, 2003. Three references added, typos corrected