Why is Orthogonal Plane Wave (OPW) Complete?

[AndrewShen]

Orthogonal plane waves can be used to expand Bloch waves. It is better than plane waves because it converges more quickly. However, I've got a problem. The completeness of plane waves is guaranteed by Fourier analysis. Why is OPW complete? It is orthogonal to core levels. But does it mean OPW is complete?

 

[bsmile]

http://encyclopedia2.thefreedictionary.com/orthogonalized+plane-wave+method

Note the statement that the trial basis wave function is constructed as linear combinations of plane waves and Bloch functions based on core states. Thus OPW is not purely plane waves.