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Results tagged with eigenvalue
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user 186099
A linear operator (including a matrix) acting on a non-zero *eigenvector* preserves its direction but, in general, scales its magnitude by a scalar quantity *λ* called the *eigenvalue* or characteristic value associated with that eigenvector. Even though it is normally used for linear operators, it may also extend to nonlinear operations, such as Schroeder functional composition, which evoke linear operations.
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What can be said about the spectrum of a Hamiltonian of a single particle confined in a box ...
Taking a look at a particular eigenvalue $E \in \sigma(H)$, we will also quickly notice that the corresponding eigenspace $\mathcal H_E$ is finite-dimensional. … Moreover, the eigenspace to each nonzero eigenvalue is finite dimensional [...] …
- 153
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Bloch's Theorem without periodic boundary condition - mathematically rigorous way
I suppose that it is possible to write any generalized eigenstate to generalized eigenvalue $E$ as some integral
$$\psi(\mathbf r) =\ "\int_{\text{some domain}} \mathrm{d}^3 \mathbf k\ \psi_{\mathbf k} … (\mathbf r)" ,$$
where the $\psi_{\mathbf k}$ are generalized eigenstates of $H$ to generalized eigenvalue $E$ and eigenstates of all Translations. …
- 153