Linked Questions
27 questions linked to/from Adding 3 electron spins
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Adding angular momenta in quantum mechanics [duplicate]
When there are two spin-1/2 particles, the possible states can be grouped into a singlet and a triplet.
When there are three spin-1/2 particles, there are two possible values for the total angular ...
- 341
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When combining three spin $\frac{1}{2}$ particles what are the corresponding states?
I want to combine three spin half particles and this is what I have so far.
I used the lowering operator $J_{-}$ on the top states and found the following states fine:
$$\left|\frac{3}{2},\frac{3}{2}\...
- 317
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How to use Clebsch-Gordan coefficients for 3 particles?
I have a Hamiltonian for 3 particles of spin 1 that I boiled down to:
\begin{equation}
k(\textbf{S}^2+\cdots),
\end{equation}
where:
\begin{equation}
\textbf{S}=\textbf{S}_1+\textbf{S}_2+\textbf{S}_3.
...
- 3,453
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2
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Tensor product decomposition of $SU(2)$ duplet representations
I have a rather trivial question. I am looking for the decomposition of $1/2\otimes 1/2\otimes 1/2$. It should give, $0,1/2$ and $3/2$. I thought one must get as the overall dimension of this space 8, ...
- 1,363
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1
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3 particles spin using Clebsch-Gordan Coefficients
I know that there are a lot of question similar to mine on this website and I have checked them all out and still can't seem to to figure this out...
If I'm adding together let's say the spins of ...
- 789
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1
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Wave functions for three identical fermions
I would like to express the wave functions for three identical particles, each with orbital angular momentum $L=1$ and spin angular momentum $S=1/2$, in terms of single-particle wave functions. In ...
- 101
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2
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Clebsch-Gordan coefficients for more than 2 particles
I need to couple arbitrary spins together and need Clebsch-Gordan coefficients for them. This should be just coupling the last two particles, then couple the next until the first particle is coupled.
...
- 8,499
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Addition of three angular momenta
To add three mutually commuting angular momenta $\mathbf{J}=\mathbf{J}_1+\mathbf{J}_2+\mathbf{J}_3$, we may follow this method: add $\mathbf{J}_1$ and $\mathbf{J}_2$ to obtain $\mathbf{J}_{12}=\mathbf{...
- 265
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1
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How do you add angular momentum of three or more particles in quantum mechanics?
I'm trying to find some information on how to add the angular momentum of three or more particles, but all the sources I look at deal with only two. In this case I understand that if the angular ...
- 749
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1
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Baryon wavefunctions
The textbook I am currently using states that when all quarks have the same flavor, there are no $J=1/2$ baryon wavefunctions for the ground state $l=0$.
Is this an experimental result or is there a ...
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Addition of 3 spin 1/2 particles
I'm trying to rationalize what it physically means to add three spin-1/2 particles. I understand that for a system of two spin-1/2 particles that there are four basis vectors in the new space on ...
- 428
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1
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Clebsch-Gordan with three particles
I am calculating normalized eigenstates for a problem with three particles, when I came across this problem:
what to do when $s_1=0$, I calculated the coefficients for
$|\downarrow\uparrow \rangle \...
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1
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Orbital angular momentum selection rules for three identical particles
I'm trying to figure out if there are selection rules for the total orbital angular momentum for a system of three identical particles, say bosons.
For two identical bosons one can argue that the ...
- 457
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Direct Sum representation of multiple particles in Quantum Mechanics
Suppose that I have three non-interacting spin-1/2 particles such that I can represent the combined system in a basis of
\begin{align}
D^{(1/2)}_1 \otimes D^{(1/2)}_2 \otimes D^{(1/2)}_3
& =\left(...
- 663
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Clebsch-Gordan coefficients for all the normalized $S_\textrm{tot}^2$ eigenstates of a three spin system with spin $s_\textrm{tot} = 1/2$?
The total spin operator is defined as $\vec{S}_\textrm{tot} = \vec{S}_1 + \vec{S}_2 + \vec{S}_3$ with $\vec{S}_1 = S\otimes\mathbb{I}\otimes \mathbb{I}$, $\vec{S}_2 = \mathbb{I}\otimes S\otimes \...
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