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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. ...
242 views

Doubt on Sakurai's proof of Wigner-Eckart theorem

In Sakurai's and Napolitano's book "Modern quantum mechanics" there's a nice proof of the theorem. This can be found also almost identical on Wikipedia's Wigner–Eckart theorem - Proof. The thing that ...
83 views

321 views

Computing reduced matrix element without Wigner-Eckart theorem

Lets have a problem: suppose we need to calculate reduced matrix element of some transition of a particle from some higher-order spin(or rather total angular momentum state, it does not really matter, ...
451 views

227 views

If momentum is the generator of translations in position space, does position act similarly in momentum space?

Since $\exp(-ia\hat{p})|x\rangle=|x+a\rangle$, do we find that $\exp(-ik\hat{x})|p\rangle=|p+k\rangle$? If so, I don't think I've seen this symmetry explicitly discussed yet, how do we interpret it? ...
943 views

Why are the generators of rotation in the 4-dimensional Euclidean space correspond to rotations in a plane?

In three-dimensions, the rotation generators are represented by $J_1$, $J_2$ and $J_3$ where $1,2,3$ respectively stands for the generator of rotation about $x,y,z$ axes respectively. In general, in ...
227 views

Connection between spin and lorentz invariance [duplicate]

I came across this statement in the book "Quantum Field theory and the Standard Model" by Matthew Schwartz. "There is a deep connection between Spin and Lorentz invariance that is obscure in Non ...
280 views

Helicity quantization of massless particles

In Appendix B of QFT in a nutshell by Zee, a review of group theory is given. In the last paragraph of the appendix on page 533, he briefly discusses the helicity quantization of massless particles. ...
187 views

6j-symbol from summing Clebsch-Gordan coefficients

I'm trying to do some three body calculations using a harmonic oscillator basis in two relative coordinates. As part of the calculations, I get a sum of a product of multiple Clebsch-Gordan ...
237 views

Quantization of angular momentum in $SO(3)$

When hermitian operators $L_1, L_2, L_3$ follow the commutation relations: $$[L_1,L_2]=i\;L_3 \\ [L_2,L_3]=i\;L_1 \\ [L_3,L_1]=i\;L_2$$ one can show that, assuming they are in finite number, their ...
2k views

Physical Interpretation of Clebsch-Gordan Coefficient

I have seen in the algebra of Angular Momentum, how Clebsch-Gordan coefficients arise. However, I do not understand the physical interpretation of it. When I checked the literature it was all in ...
129 views

135 views

Using symmetry to determine a hydrogen electron's decay route from $|300\rangle$ to $|100\rangle$

Lets say we have an electron in state $|nlm\rangle = |300\rangle$ of the hydrogen atom. By selection rules, we know that it can only decay to ground state in 3 ways, namely through the $|21m\rangle$ ...
867 views

Why is there no 1/3 spin? [duplicate]

Why do no particles have a 1/3 spin? Why are all particles' spin either a half-integer or integer? How would a particle with such a spin behave, as a fermion, boson, or neither?