Crystal momentum is a term used in solid state physics to describe the momentum of an electron in a crystal lattice. It takes into account the periodic nature of the crystal lattice and is related to the electron's velocity and position within the lattice.
Crystal momentum differs from other momentums, such as linear momentum or angular momentum, in that it takes into account the periodic nature of the crystal lattice. This means that the electron's momentum can only take on certain allowed values within the lattice.
The relationship between crystal momentum and linear momentum can be described by the Bloch theorem, which states that the electron's wavefunction in a crystal lattice can be written as a product of a periodic function and a plane wave. The crystal momentum is then proportional to the wavevector of the plane wave component of the wavefunction.
The energy of an electron in a crystal lattice is related to its crystal momentum through the dispersion relation, which describes how the energy of the electron changes with its momentum. This relationship is important in understanding the electronic properties of materials.
Yes, crystal momentum can be conserved in certain processes, such as electron-phonon interactions, where the electron may scatter off of a lattice vibration. This conservation of crystal momentum can have important consequences for the behavior of electrons in a crystal lattice.