Eigenvalues and Eigenvectors of The Second Derivative
For many combinations of boundary conditions explicit formulas for eigenvalues and eigenvectors of the second derivative can be obtained. For example, assuming and homogeneous Dirichlet boundary conditions, i.e., the eigenvalues are and the corresponding eigenvectors (also called eigenfunctions) are . Here,
For other well-known cases, see the main article eigenvalues and eigenvectors of the second derivative.
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