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# File:Lattice waves.png

## Summary

 Description Demonstration of the reciprocal lattice. A real space 2D lattice with primitive vectors ${\displaystyle a_{1}}$ and ${\displaystyle a_{2}}$, shown blue and green arrows respectively. ${\displaystyle R}$ is a general lattice vector, shown red. ${\displaystyle r}$ is a vector from the origin to any point. Plotting plane waves of the form ${\displaystyle e^{iG\cdot r}}$, we see that for any integer combination of reciprocal lattice vector basis ${\displaystyle g_{1}}$ and ${\displaystyle g_{2}}$, the resulting plane waves have the same periodicity of the lattice - that is that any translation from point ${\displaystyle r}$ to a point ${\displaystyle R+r}$, the value of the plane wave is the same. These plane waves can be added together and the above relation will still apply. Date 23 May 2020 Source Own work Author Hugh Ramsden

## Licensing

I, the copyright holder of this work, hereby publish it under the following license:

### Captions

Plane waves in a periodic lattice