##  [Bloch's Theorem](/blochs-theorem) 

  ##  [Bloch's Theorem](https://engineering.quantumdictionary.io/blochs-theorem-0) 

  

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**Engineering & Applied Technologies Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A quantum-mechanical statement that in a spatially periodic potential the eigenstates of a single electron can be written as a plane wave multiplied by a lattice-periodic function, ψ_k(r) = e^{i k·r} u_k(r), where u_k(r + R) = u_k(r) for every lattice vector R; this structure underlies band formation and the concept of crystal momentum.