# Questions tagged [matrix-elements]

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### Spin 1 Matrix Representation

I want to prove that the spin 1 matrix representations $(x,y,z)$ obey the angular momentum algebra, and i want to do it in another way. Suppose that the $x$-component of a spin 1 matrix is represented ...
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### Matrix representation of squeezing operator

In quantum mechanics we know that every operator can be represented by a matrix.Being a beginner of quantum optics, my question is does there exist a matrix for squeezing operator also? If does, can ...
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### Calculation of the decay rate of the $W$ boson

I am trying to calculate the decay rate of the $W^-$ boson to a charged lepton and the corresponding antineutrino. I denote the four momentum of the $W$ boson with $q = (M_W, \vec{0})$. The momenta of ...
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### Expectation values of fermionic operators

I'm trying to compute the matrix elements of an Hamiltonian expressed in terms of fermionic operators. The system is an Agassi model, N interacting fermions on 2 levels separated by energy $\epsilon$, ...
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### Matrix representation of Lorentz boost acting on a scalar

For the unitary translation operator $\hat{X}_a$ in 1 dimension it is easy to show that its matrix elements can be expressed purely with a delta distribution or equivalently as a combination of a ...
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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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### Numerically approximating eigenstates and energies of a particle subject to some potential. Question about dirac orthonormality and infinite terms

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 ...
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### A specific question about sakurai modern quantum mechanics

In the kronocker deltas for spin, $\lambda_4$ and $\lambda_3$ places changes. How can the author change their places? Also, I see both case can appear by calculation so there are two different ...
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### Stiffness matrix of an orthotropic transversely isotropic material

I am studying the generalized Hooke's law for an orthotropic transversely isotropic material (the same behaviour along the directions $x_2=y$ and $x_3=z$). The general elastic law by Hooke states that ...
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### Parity operator for a general $N\times N$ Hamiltonian

Assume I've a $N\times N$ tight-binding Hamiltonian that depends on spatial coordinates $k=(k_x, k_y)$; it holds $$H(k)|\psi_k\rangle = E_k |\psi_k\rangle \quad .$$ Now I want to find the parity ...
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### Indices of the Minkowski metric and Lorentz transformation

I am currently in the process of studying special Relativity and I keep stumbling over a concept I can't make consistent for myself. It is about the fact which index of a Lorentz transform and the ...
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### Issue when trying to represent an operator as a matrix

We say that a ket $|V\rangle$ can be expresed in an orthonormal basis $(|e_1\rangle,|e_2\rangle,...|e_n\rangle)$ as : $$|V\rangle = \sum_i^n v_i |e_i\rangle$$ where $v_i = \langle i|V\rangle$ for a ... For a quantum state $\Psi=c_{1}\psi_{1}+c_{2}\psi_{2}$ with momentum eigenstates $\psi_{1}$ and $\psi_{2}$, the action of the momentum operator $\hat{p}$ is given by \hat{p}\Psi=p_{1}c_{1}\psi_{1}+...