# All Questions

67 questions
Filter by
Sorted by
Tagged with
1answer
42 views

2answers
126 views

### 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. ...
1answer
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 ...
1answer
83 views

1answer
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, ...
4answers
451 views

1answer
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? ...
2answers
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 ...
1answer
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 ...
1answer
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. ...
0answers
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 ...
1answer
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 ...
2answers
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 ...
1answer
129 views

1answer
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 $|21m\rangle$ ...
1answer
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?
1answer
408 views

### Matrix represenation of total angular momentum operator

I see that for total ket in QM of hydrogen atom we define a tensor product of kets of spatial and spin spaces, upon which spatial and spin operators, operate respectively. For the total angular ...
1answer
328 views

### 3D isotropic oscillator and angular momentum algebra

In our QM class, the prof said: "We are ready to begin constructing the individual states of the 3D isotropic harmonic oscillator system. The key property is that the states must organize ...