# Questions tagged [eigenvalue]

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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### Eigenvectors and eigenvalues of a metric

Suppose we have an $n$-dim Riemannian space $V_n$ endowed with a metric. More precisely, it is defined a $(0,2)$-type tensor field in $V_n$: $$g_{\mu\nu} = g_{\mu\nu}(x),\quad x\in V_n$$ Questions. ...
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### Hamiltonian matrix for a delta potential with periodic boundary condition

I'm trying to find the energy eigenvalues of a Dirac delta potential: $$V(x)=-\alpha\delta(x)$$ with periodic boundary condition over some length $L$: $$\psi(x+L)=\psi(x)$$ and only even ...
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### Unitary Transformation of Eigenstates

Suppose I have two operators, $A$ and $B$, with eigenstates $A \lvert a \rangle = a \lvert a \rangle$ and $B \lvert b \rangle = b \lvert b \rangle$, where $a$ and $b$ are all unique. Furthermore, ...
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### What are the eigenvalues of $L_+$ and $L_-$?

I'm studying angular momentum in quantum mechanics. My question involves the operators $L_+=L_x+iL_y$ and $L_-=L_x-iL_y$; in a problem I have a Hamiltonian, $H$, depending an $L_y$, $L^2$ and $L_z$. ...