Free Electrons in Uniform Magnetic Field: Landau Levels and Quantum Hall Effect
The Zeeman effect, which we discussed in some detail in Sect. 14.2, originates from the interaction between the magnetic moment of an electron bound to an atom and a uniform magnetic field. Experimentally this effect is often observed in atomic gases but can also manifest itself with bound electrons in semiconductors and dielectrics. What is important is that the quantum states of the electrons in all these cases belong to discrete energy eigenvalues. In metals and in the conduction band of semiconductors, on the other hand, the energy levels of electrons belong to the continuum spectrum, and in some instances, electrons can even be treated as free particles. The interaction between such unbound, almost free electrons and the uniform magnetic field results in some fascinating effects which had played and are still playing an important role in physics.