The wave function at the border of Wigner-Seitz cell

[hokhani]

In the cellular method of calculating the band structure:
Why we have to take zero the normal derivative of the wave function at the Wigner-Seitz cell's border?

 

[daveyrocket]

Because of symmetry. At the faces of the Wigner-Seitz cells there is a mirror symmetry, and if the wavefunction has a non-zero derivative at that point (normal to the face) that would violate the requirement of the Schrödinger equation that the wavefunction be twice-differentiable in all space.

 

[DrDu]

Also take in mind that this only holds for the states with k=0.

 

[hokhani]

I thank both of you daveyrocket and DrDu.