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Results tagged with sp.spectral-theory
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user 132310
Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices
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Eigenfunctions of the Laplacian on $\Bbb R^d$ in Fourier space
Let $\Delta$ be the Laplacian on $\mathbb R^d$. There are no eigenfunctions of the Laplacian in $L^2(\mathbb R^d)$, but $e^{ik\cdot x}$ is an eigenfunction since
$$
\Delta e^{ik\cdot x} = -|k|^2 e^{-i …
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