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Symmetric three-spin-one subspace
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Branch of physics
Quantum mechanics
Angular momentum operator
Addition of angular momentum
Total-spin sector
Three spin-one angular-momentum decomposition
2026-09-29
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The completely symmetric subspace of three spin-one systems has
dimension
(
3
3
+
3
−
1
)
=
10
(1)
and decomposes into one total-spin-
3
multiplet
and one total-spin-
1
multiplet
:
Sym
3
(
1
)
=
3
⊕
1.
(2)
The highest-
weight
product state
generates the seven-dimensional spin-
3
multiplet
; its three-dimensional invariant complement is spin
1
.
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Three spin-one angular-momentum decomposition
Total-spin sector
Addition of angular momentum
Angular momentum operator
Quantum mechanics
Branch of physics
Physics
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Past exam of the mathematics course of the University of Cambridge
/
2020
/
ii
/
Paper 3
/
33A
/
Solution
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