8.1 Introduction

Engineers who design transistors, lasers and other semiconductor components want to understand and control the cause of resistance to current flow so that they may better optimize device performance. A detailed microscopic understanding of electron motion from one part of a semiconductor to another requires the explicit calculation of electron scattering probability. One would like to know how to predict electron scattering from one state to another. In this chapter we will see how to do this using powerful quantum-mechanical techniques.

In addition to understanding electron motion in a semiconductor we also want to understand how to make devices that emit or absorb light. In Chapter 6 it was shown that a superposition of two harmonic oscillator eigenstates could give rise to dipole radiation and emission of a photon. The creation of a photon was only possible if a superposition state existed between a correct pair of eigenstates. This leads directly to the concept of rules determining pairs of eigenstates which can give rise to photon emission. Such selection rules are a useful tool to help us understand the emission and absorption of light by matter. However, the real challenge is to use what we know to make practical devices which operate using emission and absorption of photons. This usually requires imposing some control over atomic-scale physical processes which, of course, can only be understood using quantum mechanics.

Our study begins by considering electronic transitions due to an abrupt time-dependent change in potential. Following this, we will derive...