3 Born–Oppenheimer approximation
In this chapter, we develop the basic framework to see how electron–electron (e-e), electron–ion (e-i), and ion–ion (i-i) interactions affect the properties of solids. We first show that the electron and ion degrees of freedom can be decoupled. Such a separation arises because ions and electrons have vastly different velocities in a solid; roughly, the electron velocity is 1000 times larger than the ion velocity. As a consequence, the electrons view the ions as providing a static background in which they move. This physical picture is at the heart of the Born–Oppenheimer approximation (BO1927).
3.1 Basic Hamiltonian
It useful at the outset to consider the total Hamiltonian to understand how to separate the ...