Concept

Bloch's theorem

Summary
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions. The theorem is named after the physicist Felix Bloch, who discovered the theorem in 1929. Mathematically, they are written where \mathbf{r} is position, \psi is the wave function, u is a periodic function with the same periodicity as the crystal, the wave vector \mathbf{k} is the crystal momentum vector, e is Euler's number, and i is the imaginary unit. Functions of this form are known as Bloch functions or Bloch states, and serve as a suitable basis for the wave functions or states of electrons in crystalline solids. Named after Swiss physicist Felix Bloch, the description of electrons in terms of Bloch functions, termed Bloch electrons (or less often Bloch Waves), underlies the concept of electronic band structures. T
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