Questions tagged [matrix-elements]
Matrix elements are the components, or entries, of a matrix, typically considered in a certain basis.
262 questions
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Injective MPO representation of the exponential of the Ising model
According to these Les Houches lecture notes (page 12), it is possible to find an injective, bond dimension 2 MPO representation of the exponential of the quantum Ising Hamiltonian (with no external ...
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Matrix element of order $n$ [closed]
Does anyone know an explicit formula to calculate the following matrix element? It is in the context of quantum optics,
$$\langle\alpha | a^n \mathcal{D}(\beta) | m\rangle,$$
where $|\alpha\rangle$ is ...
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Wrong indices in tensor transformation under rotation [closed]
So here is a snippet from my notes
First of all I'm assuming that if $d_i v_j + d_jv_i$ is a tensor then $d_iv_j $ should also be a tensor.This is for simplicity
So here is my attempt to solve it. So ...
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What is the correct term for this quantity?
I am dealing with direct and exchange Coulomb matrix elements in periodic systems.
When computing these, there are terms within that look like this:
$$\rho_{ik} (\mathbf{r}) = \phi_{i}(\mathbf{r}) \...
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The $SU(2)$ $F$-matrix for $\tfrac{1}{2} \otimes \tfrac{1}{2} \otimes \tfrac{1}{2} \to \tfrac{1}{2}$ and quantum dimension
I'm working through $SU(2)$ angular momentum coupling and trying to compute the $F$-matrix (recoupling isomorphism) associated with three spin-$\tfrac{1}{2}$ particles coupled to a total spin of $\...
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Hermicity not preserved in Hamiltonian [closed]
My question is in the context of a matrix element in a diatomic molecule. I will rephrase it as well as possible to remove any unnecessary complexity.
I denote the spherical harmonic as $Y_m^l = |m,l\...
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Boundary conditions in the finite element method for the Helium atom
In the following paper, the authors obtain the ground state of the helium atom (-2.9032) using the finite element method. The paper can be downloaded here (https://drive.google.com/file/d/...
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Matrix Element of angular Momentum and Vector Operator
I am reading the book The Theory of Atomic Spectra by E. U. Condon and G. H. Shortley. On page 60, they claim that the matrix element of the operator
$$\sum_{j=1}^3\langle j'm'|J_i J_j T_j|jm\rangle$$
...
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Why do we use matrix in physics? [closed]
I recently started learning theoretical physics by myself and my book (the theoretical minimum series), and in this book, hessian matrix is used for multivariable function, and i want to know that why ...
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Can the projection in the completness operator be applied multiple times in the integral
I'm trying to rewrite the matrix element $\langle k | V |k' \rangle$ of the potential V in terms of position space using the completeness relation.
I know that the completeness relation in position ...
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Help finding matrix elements for $SU(3)$ tensors
I'm trying to solve the following problem:
Find the matrix elements $\langle u|T_a|v \rangle$ where $T_a$ are the $SU(3)$ generators and $|u\rangle$ and $|v\rangle$ are tensors in the adjoint ...
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Possible errata Landau and Lifshitz in $\S29$ Matrix elements of vectors in Quantum Mechanics Third Edition [closed]
Context
L&L write,
Let $\mathbf{A}$ be some vector physical quantity characterizing a closed system... In the particular case where $\mathbf{A}$ is the radius vector of the particle... we find ...
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Physical interpretation of the matrix element
In perturbation theory, but also in other scenarios the claim is made that the following expression:
$|\langle f|\hat O||i\rangle|^2$ represents the probability amplitude for a transition of the ...
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Meaning of Fourier expansions in Heisenberg's matrix mechanics [closed]
I am trying to figure out the passages Heisenberg followed in developing matrix mechanics as presented in his 1925 Umdeutung paper. In developing the virtual oscillators model, Heisenberg uses the ...
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What subset of the Lorentz group produces a given Weyl spinor?
Let's say I have a unit Weyl spinor $\psi = [\psi_1\ \psi_2]^T$. This has 3 degrees of freedom. Now suppose that this spinor was produced from a reference unit spinor — let's take $[1\ 0]^T$ to be ...
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