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This tag is for questions regarding to the boundary conditions (b.c.) which expresses the behaviour of a function on the boundary (border) of its area of definition. The choice of the b.c. is fundamental for the resolution of the computational problem: a bad imposition of b.c. may lead to the divergence of the solution or to the convergence to a wrong solution.
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Counting $k$-states with periodic or fixed boundary conditions
When counting $\vec k$-states in a system - in my case, counting the number of states in the first Brillouin Zone - we either use periodic boundary conditions, $$\psi(\vec r) = \psi(\vec r + \vec L)$$ …