Magnetic Flux Quantization of the Landau Problem

Landau problem has a very important application in modern physics, in which two-dimensional electron gas system and quantum Hall effect are outstanding. In this paper, first we review the solution of the Pauli equation, then using the single electron wave function, we calculate moving area expectations of the ideal 2-dimensional electron gas system and the per unit area's degeneracy of the electron gas system. As a result, how to calculate the magnetic flux of the electron gas system is given. It shows that the magnetic flux of 2-dimensional electron gas system in magnetic field is quantized, and magnetic flux quantization results from the quantization of the moving area expectations of electron gas system.