The scale at which a series of potentials froms _periodic potential_ is determined by the [de Broiglie wavelength](Stationary%20Quantum%20Systems%20(Index).md#Debroiglie%20wavelengths) of whatever [quantum system](Quantum%20systems.md) is subject to that potential. For example, for [electrons](Periodic%20potentials.md#Electrons%20in%20crystal%20lattices) the de Broiglie wavelength is typically at the scale of $10^{-8}$ m.
# Geometry of periodic potentials
## Lattice vectors and reciprocal lattices
For [Bravais lattices](Bravais%20lattices.md) in three dimensions we define the [lattice vectors](Bravais%20lattices#^a50b5e) in three spatial dimensions as [$\mathbf{R}=n_1\mathbf{a}_1+n_2\mathbf{a}_2+n_3\mathbf{a}_3$](Bravais%20lattices#^cd8772) ^13f06b
and the _reciprocal lattice_ is described by [$\mathbf{k}=x_1\mathbf{b}_1+x_2\mathbf{b}_2+x_3\mathbf{b}_3$](Bravais%20lattices#^0fdaee) where [$\mathbf{b}_i\mathbf{a_j} = 2\pi\delta_{ij}$](reciprocal%20lattices#^526884) ^1fe7d8
# Square-well periodic potentials
# Wavefunctions in periodic potentials and Bloch's theorem
([... see more](Bloch's%20theorem.md))
## Kronig-Penney model
([... see more](Kronig-Penney%20model.md))
# Physical realizations of periodic potentials
## Electrons in crystal lattices
#QuantumMechanics/StationaryStateQuantumSystems
#QuantumMechanics/MultiParticleQuantumSystems/SolidStatePhysics