Section 7.1 Introduction
The basics of quantum mechanics and its interpretation can be understood by first looking at one-dimensional problems. This is what we have done so far in this unit. But the real world has three spatial dimensions, and most real systems have more than one particle to keep track of. The extension of the Schrödinger equation to three dimensions is straight-forward, but the math can get a little complicated.
We will confine our study primarily to the case of electrons in atoms. A key feature of wavefunctions in three dimensions (3D) is that the allowed quantum states are described by three quantum numbers instead of one. For the states of electrons in atoms, each quantum number has a distinct physical interpretation, as we will see.
Also in this chapter we describe the basics of semiconductor physics, which follows from the discussion of energy bands in Chapter 4. We will explain how the conductivity of materials can be understood in terms of these bands, and we'll discuss how these quantum properties have led to some really cool (and tremendously important) techniques that form the basis of modern electronics.