Non-interacting Electrons

Abstract

Most properties of a crystal may be interpreted as the quantum mechanical motion of a single electron in a given potential. After the simplest cases of motion in homogeneous electric and magnetic fields with emphasis on the thermodynamic limit, an extended treatment of the motion in a periodical potential is given. The Bloch oscillations observed in periodical semiconductor layers are also included. The ground state occupation of the one-electron states leads to the understanding of the different classes of materials, as metals, insulators and semiconductors. The properties of the latter are strongly influenced by the presence of impurities. The controlled presence of donors and acceptors determine the properties of semiconductor contacts discussed on the example of a p-n contact.