High Quality Content by WIKIPEDIA articles! Explicit formulas for eigenvalues and eigenvectors of the second derivative with different boundary conditions are provided both for the continuous and discrete cases. In the discrete case, the standard central difference approximation of the second derivative is used on a uniform grid. These formulas are used to derive the expressions for eigenvalues and eigenvectors of multidimensional discrete Laplacian on a regular grid, which is presented as a Kronecker sum of discrete Laplacians in one dimension.

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