Blochvågorna

Blochvågorna, named after the physicist Felix Bloch, are solutions to the Schrödinger equation for electrons in a periodic potential, such as that found in crystals. These waves describe the behavior of electrons in a lattice structure. A key characteristic of Blochvågorna is that they are modulated plane waves. This means that their amplitude is not constant but varies periodically with the same periodicity as the crystal lattice. Mathematically, a Bloch wave can be represented as a product of a plane wave, e^(ikx), and a periodic function, u_k(x), where k is the wavevector and has the same periodicity as the lattice.

The wavevector k in a Bloch wave is crucial. It is not necessarily the same as the wavevector of a free electron because the periodic potential modifies the electron's motion. The wavevector k determines the electron's energy and momentum within the crystal. The set of all possible k values forms the reciprocal lattice. The periodicity of the Bloch waves is directly linked to the translational symmetry of the crystal lattice. When an electron encounters the periodic potential, its wave function adapts to this structure, leading to the formation of Blochvågorna. This concept is fundamental to understanding the electronic properties of solids, including electrical conductivity and the formation of energy bands.