## Basic Equations of Electrodynamics

The Maxwell equations are remarkably structured. If it were not for the absence of magnetic charges in nature, we would be able to exchange the roles of the electric field E and the magnetic field H , as well as the electric displacement D and the magnetic induction B . We first write the Maxwell equations in differential form each equation must be satisfied in every point of space Each of the equations can be integrated over space, and after applying some vector identities we obtain the...

## Px x Wx tWx t

For the electron described in terms of a wavefunction it is the average value of its position In this case X is called the position operator. We shall use to identify operators whenever we are not dealing with a special representation. In the position representation X is a vector with cartesian components x, y and z. The result of (3.3) gives the most probable position where to find a particle. It is called the expectation value of the position operator. It is...

## The Vibrating Uniform Lattice

The elastic, spring-like nature of the interatomic bonds, together with the massive atoms placed at regular intervals these are the items we isolate for a model of the classical mechanical dynamics of the crystal lattice see Box 2.3 for brief details on Lagrangian and Hamiltonian mechanics . Here we see that the regular lattice displays unique new features unseen elsewhere acoustic dispersion is complex and anisotropic, acoustic energy is quantized, and the quanta, called phonons, act like...

## Free and Bound Electrons Dimensionality Effects

Another more sophisticated point is the fact that the energy spectrum may show a both discrete and a continuous part. This leads us to the following question How does the spectrum depend on the imposed boundary conditions To determine finally the functional form of the wavefunction, we need information about these boundary conditions that the electronic system has to fulfill. The resulting spectrum of observables will be discrete, continuous or mixed and allows us to talk about its...

## Electron Distribution Functions

The distribution functions for electrons in the periodic lattice of a semiconductor follow Fermi-Dirac statistics. To distribute a certain number of electrons in the conduction band of a semi-conductor, we have to know the shape of the band with respect to the momentum of the electron, as explained in Section 3.3.3. An intrisic semiconductor is a pure crystal, where the valence band is completely occupied and the conduction band is completely empty. This is the whole truth for a purely...

## Quantum Mechanics of Single Electrons

Quantum mechanics describes the fundamental properties of electrons 3.1 , 3.2 . It tells us that both particle-like and wave-like behavior is possible. In a semiconductor both types of behavior are observable. The particle concept turns out to be an excellent description for a wide range of classical phenomena and the most common applications. Modern devices on the nanometer scale instead demonstrate the quantum nature of electrons in many beautiful ways. Their deeper understanding requires a...