The Quantum Hall Effects

Abstract This chapter first analyses the integer quantum Hall effect, covering an electron in two dimensions in a magnetic field; a two-dimensional electron gas in a magnetic field; motion under orthogonal electric and magnetic fields; the quantization of the Hall voltage; an electron in two dimensions in a magnetic field; edge states; and localized states. The chapter then turns to the fractional quantum Hall effect, discussing a semi-empirical accounting for observed filling fractions; many-body ground states for non-interacting electrons in the lowest Landau level; adding flux tubes to the non-interacting many-body ground state wave function; and trial ground states for the fractional quantum Hall effect. Sample problems are also provided at the end of the chapter.