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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Symbol denoting parity eigenvalue
What is the symbol reserved for designating the parity of a parity eigenstate?
For example an eigenstate $\phi$ of the squared angular momentum operator $\hat{\mathbf{L}}^2$ is characterized by a ...
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Eigensystem of part of the representation of the position operator: $a^\dagger+a$ in the base of the quantum harmonic oscillator [closed]
What are the exact eigenvalues and eigenvectors of the following matrix?
\begin{equation}
\begin{pmatrix}
0&\sqrt{n}&0&\cdots&0&0\\
\sqrt{n}&0&\sqrt{n+1}&\cdots&0&...
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How can I interpret the normal modes of this mechanical system?
How can I interpret the normal modes of this mechanical system?
The equations of motion for the system are as follows:
$$\left[\begin{array}{ccc}
m_{1}\\
& m_{2}\\
& & 0
\end{array}\...
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The eigenvectors associated to the continuous spectrum in Dirac formalism
I am comfused about the definition of an observable, eigenvectors and the spectrum in the physics litterature. All what I did understand from Dirac's monograph is that the state space is a complex ...
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Decoupling Linearly Coupled Wave Equations with Potentials
I'm currently working numerically with wave equations and I was wondering if one can always decouple two wave equations, with potentials, which are linearly coupled. The system I'm talking about is ...
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Green function in scattering theory
I'm having a bit of trouble with a step in scattering theory.
Context:
The Schrödinger equation for a two-body scattering problem can be written as:
$$
(E - H_0) |\psi\rangle = V |\psi\rangle.
$$
Here,...
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Bogoliubov de Gennes formalism for rotating systems
I have a question relating to the Bogoliubov de Gennes formalism. I am studying Bose Einstein condensates and I want to calculate the excitation energies of a system in one dimension (a ring with ...
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Calculating Eigenkets of Perturbed Matrix for Second-Order Correction
Q: Find the eigenvalues of the 3x3 symmetric matrix $H$ using perturbation theory where all of the elements on the diagonal of $H$ are an order greater than the elements not on the diagonal.
We can ...
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What is the physical interpretation of the eigenvalues of the Maxwell stress tensor?
The Wikipedia page on Maxwell stress tensor has a section on the eigenvalues of the Maxwell stress tensor, which is given by
$$ \mathrm{Eig}\{\mathbf{T}\} = \left\{ -\left(\frac{\epsilon_0}{2}E^2+\...
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Different definitions of resolvent in matrix model
When I study the matrix models, I get confused of different definations of resolvent. After we define the partition function as
$$Z=\int[dM]e^{-NTrV(M)},$$
where $V(M)$ is a matrix valued function of $...
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Why does applying Ladder operators change the eigenfunction?
When applying a ladder operator to a spherical harmonic function, it spits out the function with a lower or higher magnetic quantum number.
My question is how does this abide by the classical ...
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"Eigenvalue" in Statistical Mechanics
In Pathria's "Statistical Mechanics", 3rd ed., on page 41, he is going over a discussion of the canonical ensemble and lays out the following definitions:
$$
\mathcal{N}=\sum_rn_r \quad \...
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Difference between the expectation value of an operator and operator applied to wave function?
Expectation value of any operator $\hat{Q}$ is defined as,
$$
\left\langle\psi_n\mid\hat{Q}\mid \psi_n\right\rangle
$$
and action of the operator $\hat{Q}$ on wavefunction is defined as
$$
\hat{Q} \...
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Eigenstates of spin-1 Hamiltonian involving $x,y,z$ components
I am trying to find the energy eigenvalues and eigenstates of the spin-1 system with Hamiltonian operator
$$H \enspace = \enspace a J_z^2 + b( J_x^2 - J_y^2 ) \quad , \qquad a, b \in \mathbb{R}$$
or ...
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Momentum Eigenstates for Particle in a Box [closed]
The following lines as attached as photos taken from Beiser Modern Physics (6th Edition):
Now these equations and wavefunctions make no sense to me at all, first of all how are these wavefunctions ...
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