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# Questions tagged [matrix-elements]

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### Finding the eigenvalues and eigenvectors of this operator

The operator $$\mathcal{\hat{G}} = (\xi - 1) \sum_{j=1}^N \int dk_j \; k_j \hat{a}^\dagger_j(k_j)\hat{a}_j(k_j),$$ is physically similar to the momentum operator in quantum mechanics. It has the ...
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### Partial completeness relation for Dirac spinors

in studying trace techniques to obtain matrix elements, I came across a problem when we treat scattering of neutrinos on protons. Indeed, since those neutrinos are supposedly created in a weak decay, ...
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### What is the point of degenerate perturbation theory in quantum mechanics?

What is the point of degenerate perturbation theory in quantum mechanics? Let's disregard for a moment the issue of constructing the perturbed wave functions and assume that the 1st order correction ...
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### How to express continuous values as a matrix

Usually a quantity of a matrix is defined as the eigenvalues of the matrix. If so, how can anyone express continuous values, as in Schrodinger picture, into a matrix?
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### Matrix Representations of Quantum States and Hamiltonians

I am a high school student trying to teach himself quantum mechanics just for fun, and I am a bit confused. As a fun test of my programming/quantum mechanics skill, I decided to create a computer ...
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### Creation and Annialation Operators and Kinetic Energy Matrix Elements

I'd like to write equations for $c_{ij}(t)$, With a hamiltonian of the form $$H=\sum_{kn}a^{\dagger}_k t_{kn}a_n + \frac{1}{2}\sum_{klmn}a^{\dagger}_k a^{\dagger}_l v_{klmn}a_m a_n$$ with $t_{kn}$ ...
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### If the S-matrix has symmetry group G, must the fields be representations of G?

If the fields in QFT are representations of the Poincare group (or generally speaking the symmetry group of interest), then I think it's a straight forward consequence that the matrix elements and ...
### Vector space of $\mathbb{C}^4$ and its basis, the Pauli matrices
How do I write an arbitrary $2\times 2$ matrix as a linear combination of the three Pauli Matrices and the $2\times 2$ unit matrix? Any example for the same might help ?
This question is mostly about how to interpret notation used in Particle Physics. I am given that at lowest order the rate of $b\rightarrow s\gamma$ is proportional to \$\langle B_p|b^\dagger b|B_p\...