Abstract
The study of the electronic properties of quasi two dimensional systems has been a very exciting area of condensed matter physics during the last quarter of the 20th century. Among the most interesting discoveries in this area are the incompressible states showing integral and fractional quantum Hall effects. Incompressible quantum liquid states of the integral quantum Hall effect result from an energy gap in the single particle spectrum. The incompressibility of the fractional quantum Hall effect is completely the result of electron–electron interactions in a highly degenerate fractionally filled Landau level. Since the quantum Hall effect involves electrons moving on a two dimensional surface in the presence of a perpendicular magnetic field, we begin with a description of this problem.
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