A Bloch wave or Bloch state is the wavefunction of a particle (usually, an electron) placed in a periodic potential. It consists of the product of a plane wave and a periodic function u_nk(r) which has the same periodicity as the potential: In the most restricted usage in quantum mechanics, the wavefunction associated with a particle such as an electron, is a complex-valued square integrable function ψ defined over a portion of space and normalized in such a way that In Max Borns probabilistic interpretation of the wavefunction, the amplitude squared... Properties The electron is a subatomic particle. ... In the physics of wave propagation (especially electromagnetic waves), a plane wave (also spelled planewave) is a constant-frequency wave whose wavefronts (surfaces of constant amplitude and phase) are infinite parallel planes normal to the propagation direction. ...

The plane wave wavevector k (multiplied by Planck's constant, this is the particle's crystal momentum) is unique only up to a reciprocal lattice vector, so one only needs to consider the wavevectors inside the Brillouin zone. For a given wavevector and potential, there are a number of solutions, indexed by n, to Schrodinger's equation for a Bloch electron. These solutions, called bands, are separated in energy by a finite spacing, called the band gap. The band structure is the collection of energy eigenstates within the first Brillouin zone. All the properties of electrons in a periodic potential can be calculated from this band structure, at least within the independent electron approximation. Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ... In crystallography, the reciprocal lattice of a Bravais lattice is the set of all vectors K such that for all lattice point position vectors R. The reciprocal lattice is itself a Bravais lattice, and the reciprocal of the reciprocal lattice is the original lattice. ... In mathematics and solid state physics, the first Brillouin zone is the primitive cell in the reciprocal lattice in momentum space. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ... In solid state physics and related applied fields, the band gap is the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. ... In solid state physics, the electronic band structure (or simply band structure) of a solid is the series of forbidden and allowed energy bands that it contains. ... In mathematics and solid state physics, the first Brillouin zone is the primitive cell in the reciprocal lattice in momentum space. ...

It can be shown that the wavefunction of a particle in a periodic potential must have this form by proving that translation operators (by lattice vectors) commute with the Hamiltonian. This result is called Bloch's Theorem. In physics, a translation is the operation changing the positions of all objects according to the formula where is a constant vector. ... In geometry and crystallography, a Bravais lattice is an infinite set of points generated by a set of discrete translation operations. ... The Hamiltonian, denoted H, has two distinct but closely related meanings. ...

The concept of the Bloch state was developed by Felix Bloch in 1928. This page only addresses the German physicist, for other usages, see Felix Bloch (disambiguation) Felix Bloch, Courtesy of Nobelprize. ... 1928 was a leap year starting on Sunday (link will take you to calendar). ...