# Questions tagged [matrix-elements]

Matrix elements are the components, or entries, of a matrix, typically considered in a certain basis.

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### Non-linear sigma model quantization

Given the following lagrangian for the non-linear sigma model: $$\mathcal{L}=\frac{1}{2}\sum_{a,b}\partial_\mu\phi^a\partial^\mu\phi^b f_{ab}(\phi)$$ where $f_{ab}(\phi)$ is a matrix function. My ...
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### How to convert the following Matrix equation to tensor notation?

Consider the following equation : $$\Lambda^{-1}\Lambda^T \Lambda=A$$ Here $\Lambda$ are my lorentz transformations such that $\Lambda^T \eta \Lambda=\eta$. $A$ is some matrix. I know that in terms of ...
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### Breaking product of three vectors into symmetric and anti-symmetric vectors [closed]

Let's consider we have three arbitrary vectors A, B and C. We have the quantity $A_{\mu}B_{\nu}C_{\rho}$. Is it possible to break the above quantity into sum of symmetric and anti-symmetric vectors in ...
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### How can I demonstrate that, in a degenerate system, if $[H_0,\lambda H_1] = 0$ then $H_1$ is already diagonalized?

In the context of degenerate perturbation theory, for a perturbed Hamiltonian $H_0 + \lambda H_1$, I've heard of a very useful tool: "If $[H_0,\lambda H_1] = 0$ holds (both parts of the ...
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### Confusion regarding Fermi's golden rule

The Fermi Golden Rule is: $$\Gamma_{i\to f}=\frac{2\pi}{\hbar}|\langle f|H'|i\rangle|^2\rho(E_f)$$ In this equation, $|\langle f|H'|i\rangle|$ is giving information about the coupling. However, $f$ ...
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### Why is this rearrangement of factors in the Compton Scattering matrix element valid?

I've been trying to follow through this derivation of the total squared matrix element for Compton scattering. We have two first-order diagrams: Using Feynman rules, the matrix elements for each ...
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### Simplify calculation for matrix elements in quantum electrodynamics

So I am learning quantum field theory. At the moment I have a look at the interactions between electrons/positrons and photons, which is quantum electrodynamics. I want to calculate matrix elements of ...
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### Transforming the field strength tensor - Why do we need to use $\Lambda^T$, instead of a row times row multiplication?

The transformation law is \begin{align} F'^{\mu\nu} = {\Lambda^{\mu}}_{\alpha} {\Lambda^{\nu}}_{\beta} F^{\alpha \beta} = {\Lambda^{\mu}}_{\alpha} F^{\alpha \beta} {\Lambda^{\nu}}_{\beta} \end{align} ...
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### Why can we use $Tr(AB) = Tr(A)Tr(B)$ when finding matrix element squared? [closed]

Here is a $t$-channel Feynman diagram I'm working on: Using Feynman's rules, we can find the matrix element as  M_t = -ig^2\frac{\bar u^{s_3}(p_3)u^{s_2}(p_2)\bar u^{s_4}(p_4)u^{s_1}(p_1)}{(p_2-p_3)...
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### The Physical Meaning of Variance of Random Matrix Entries

I am trying to make some physical sense of the Hamiltonian described on pages 1, 2 here. The part I don't get is in the image attached below. I understand what the variance of each entry term tells me ...
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### How to reduce matrix element of a spherical tensor operator?

I am studying about Wigner-Eckart theorem, and I have a question about the reduced matrix element. Wigner-Eckart theorem: (I follow the terms as in Wikipedia, https://en.wikipedia.org/wiki/Wigner%E2%...
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### Hamiltonian as a matrix and its elements [closed]

Let us consider an electron in an infinitely deep one-dimensional potential well of thickness L with zero potential energy at the bottom of the well. The normalised eigenfunction solutions to this can ...
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Context I am attempting to approximate the eigenstates and energies of a particle over an interval $[-a,a]$ subject to some potential. The goal is then to approximate the wavefunction $\Psi$ with ...