Questions tagged [wigner-eckart]
The Wigner–Eckart theorem relates matrix elements of spherical tensor operators in the basis of angular momentum eigenstates to Clebsch–Gordan coefficients. Within a given subspace, a component of such operators behaves proportionally to the same component of the angular momentum operator itself. Do not use for plain Clebsch–Gordan decompositions.
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How to go from a vector operator to its components?
(I'm sorry if this question is a duplicate, I couldn't find anything that answered my question.)
I'm doing an exercise where I'm supposed to get the matrix elements for the vector operator $D$ (the ...
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Help with Wigner-Eckert Theorem problem
Currently trying to solve the following problem:
Consider an operator $O_x$ for $x = 1$ to $2$, transforming according to the spin $1/2$ representation as follows:
$$ [J_a, O_x] = O_y[\sigma_a]_{yx} / ...
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Wigner-Eckart theorem in classical physics?
The Wigner-Eckart theorem is a useful result in quantum physics and its many applications. Most presentations of this material in books on QM and online lecture notes seem to be variations on the same ...
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Wigner-Eckart for Finite groups
We know the Wigner-Eckart theorem generalizes to say $\mathrm{SU}(3)$ (see for example this answer). In a different direction, I am curious if/how it generalizes to finite groups of $\mathrm{SU}(2)$.
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Wigner-Eckart theorem for exponentiated vector operator?
Consider the Hamiltonian of two spinning particles in a magnetic field with $$H = \vec{B}\cdot\vec{\mu}$$ where $$\vec{\mu} = \alpha \vec{L}_1+\beta\vec{L}_2$$
Now I wish to compute its partition ...
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Wigner-Eckart theorem: Completeness relation
Consider the Wigner-Eckart theorem given by
$$\langle \alpha' j m'|A^q|\alpha j m\rangle = \frac{\langle \alpha' j m'|\mathbf{J}\cdot\mathbf{A}|\alpha j m\rangle}{j(j+1)}\langle j m'| J^q|j, m\rangle$$...
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Confusion regarding the Clebsch-Gordan coef. in the Wigner-Eckart theorem
I will start by giving a brief explanation to the Clebsch-Gordan coef. It's because how I perceive this coef. that I don't understand the Wigner-Eckart theorem.
The Clebsch-Gordan coefficient related ...
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