# 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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### Eigenvalue and Eigenfunction for a particle trapped in a 1D infinite asymmetric potential well

As we're barely scratching the surface of Quantum Physics in class, we haven't been taught about asymmetric potential wells. However, I find it fascinating, moreover difficult, to find the eigenvalues ...
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### Do eigenstates of the creation operator actually exist?

Regarding the eigenstate of creation operator $\hat{a}^\dagger$, the answer to this question shows that the eigenstate does not exist. However, it is stated in another answer, that the proof has ...
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### Diagonalizing eigensystem to find normal modes of coupled oscillator

I've two equations of motion that arose in a coupled oscillators in a magnetic field $\rightarrow$ continuum problem in classical mechanics: \begin{eqnarray*} -\omega^2 X &=& - \omega_0^2 X (2 ...
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### How to identify the multimodes of an optical fiber?

I use Lumerical mode software to simulate a photonic crystal fiber of NANF type. The solver gives me a lot of modes (solutions). I want to know how to know if this fiber is a single mode fiber or ...
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### Weird quantum linear operator [closed]

For a problem sheet at uni, I need to find eigenvalues and normalised eigenstates of a linear operator. This operator is $\hat{Q}$ and is defined by its action on the normalised eigenstates of the ...
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### Diagonalization of a Hamiltonian in a transformed reference frame

Under a time-dependent transformation $V(t)$ of the state vectors $|{\psi}\rangle$ \begin{equation} |\psi'(t)\rangle = V(t) |\psi(t)\rangle \end{equation} The Hamiltonian $H(t)$ has to transform as \...
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### What is modal analysis?

I know what modal analysis is, and I know how to conduct one. I can get the eigenvalues and vectors (modes). Not a problem. However, I am lost at trying to understand the philosophy of what it is. By ...
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### Commutation rules of field operators and Dirac delta

My question concerns the commutation rules between bosonic fields operators in the case in which the bosons can assume only discrete positions. I have organised this post in two sections, in the ...
A quantum-mechanical "density" matrix is Hermitian (self-adjoint), positive definite, having trace 1. In terms of its four ordered eigenvalues ($\lambda_1 \geq \lambda_2 \geq \lambda_3 \geq \... 2answers 64 views ### Solving for the momentum from eigenfunctions When you have a solution to a time-dependent Schrodinger Equation, $$\Psi(x,t)=\exp\left({-\frac{i\hbar^2k_0^2t}{2m}}\right)\sin(k_0x), \tag{1}$$ and want to know the distribution of momentum at time ... 2answers 130 views ### Meaning of Eigenvalues for position operator To each observable in quantum mechanics there is an operator corresponding to it. I don't understand what's the meaning of the eigenvalues of the$\hat{x}$operator. Since$\hat{x}$is hermitian, ... 1answer 59 views ### Doppler as an eigenvalue of the Lorentz transformation It is a known fact that $$\gamma (1\pm\beta) = \sqrt\frac{1\pm\beta}{1\mp\beta}$$ is an eigenvalue of the Lorentz transformation (which is a linear transformation). This is also (as stated in the ... 1answer 91 views ### Shared eigenbasis of commuting Operators Suppose I have two Hamiltonian pieces$H_1$and$H_2$such that$[H_1,H_2]=0$. Then we know that the two pieces have shared eigenbasis. Assume both$H_1$and$H_2$have eigenvalues 2 and -2. Let$|\...
I have been working through a problem. It has asked me to determine the eigenstates and corresponding eigenvalues of the number operator in a quantum harmonic oscillator; $$\hat{n}=\hat{a}_+\hat{a}_-$$...