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Results tagged with eigenvalue
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user 195953
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.
3
votes
The Eigenvalue problem
The operator $(\Omega - \omega I)$ can be seen as a matrix. But to be inversible, a matrix needs its determinant to be non-zero. Why does it need to be non-zero ?
Let's take a matrix A, which we'll …
- 155
0
votes
Show that normable eigenstates are not degenerated in 1D
You're on the right track !
\begin{equation}
0 = \psi_1 \psi_2'' - \psi_2 \psi_1'' = (\psi_1 \psi_2' - \psi_2 \psi_1' ) '
\end{equation}
meaning the () in the right term must be a constant :
\begi …
- 155