Band structure- implement Bloch boundary condition

hallo all,
How do I implement bloch boundry condition: f(x=0)=f(x=L)*exp(ikL) in the second derivative matrix representation (in a 1D problem) that operates on a vector: x=linespace(0,L,1000)?
where f would be some eigen function of the Laplacian matrix(written here without the bloch boundry condition ):
Lap= (-2*diag(ones(N,1),0) + diag(ones((N-1),1),1) ...
+ diag(ones((N-1),1),-1))/(dx^2);
thanks

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2020년 2월 22일

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