tejas777 said:In the so called repeated zone scheme (also sometimes called the extended zone scheme) the free electron dispersion in the periodic potential will look like a set of parabolas shifted by the reciprocal lattice vector along the k-axis.
taffara_121 said:Hi there,
Could anybody explain how the free electron dispersion relation would be modified by the presence of a periodic potential..? I'm struggling to get my head around it.
Thanks!
The free electron dispersion relation is a mathematical equation that describes the energy and momentum of an electron in a solid material. It shows how the energy of an electron changes as its momentum changes.
The free electron dispersion relation is derived from the Schrödinger equation, which describes the behavior of quantum particles such as electrons. It takes into account the periodicity of the crystal structure and the potential energy of the electrons.
The free electron dispersion relation tells us that the energy levels of electrons in a solid are quantized, meaning they can only have certain discrete values. It also shows that the energy of an electron increases as its momentum increases.
The free electron dispersion relation plays a crucial role in determining the electrical conductivity of a material. It shows that in a material with a high density of free electrons, such as a metal, the electrons can easily move and conduct electricity. In contrast, in a material with a low density of free electrons, such as an insulator, the electrons are tightly bound and cannot move as easily, resulting in lower conductivity.
Yes, the free electron dispersion relation is an important tool in predicting the properties of different materials. By understanding the energy and momentum of electrons in a material, we can make predictions about its electrical conductivity, thermal conductivity, and other properties. This information is crucial in designing new materials for various applications.