Tensor coupling and 6j/9j symbols

Tensor coupling is a mathematical concept used in quantum mechanics to describe the coupling of angular momenta between two particles or systems. It involves the use of 6j/9j symbols, which are graphical representations of the coupling coefficients between different angular momenta. These symbols are important in calculating transition probabilities and selection rules for quantum mechanical systems. They also play a crucial role in the study of molecular vibrations and rotations. In summary, tensor coupling and 6j/9j symbols are essential tools in the field of quantum mechanics, providing a way to mathematically describe the interaction between angular momenta in physical systems.
  • #1
Yoran91
37
0
Hi everyone,

I'm reading about the Wigner-Eckhart Theorem and the coupling of spherical tensor operators in Sakurai's Advanced Quantum Mechanics.
I then came across this http://cc.oulu.fi/~tf/tiedostot/pub/kvmIII/english/2004/09_tensop.pdf, which states these concepts in Theorem 1 and 3.

I'm now trying to find a connection between this coupling of tensor operators and 6j and 9j symbols. In the above document, such a link is established in the very last line, but I don't quite understand it. Nothing like this is mentioned in Sakurai and I can't find any other source that provides how these things are connected.

Is there a good source discussing this?
Thanks in advance for any help
 
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  • #2
It's derived (more or less) in the "Angular Momentum in Quantum Mechanics" book by Edmonds. Sect 7.1, Matrix Elements of the Tensor Product of Two Tensor Operators.
 

1. What is tensor coupling?

Tensor coupling is a mathematical technique used in quantum mechanics to describe the interaction between two or more particles. It involves the use of tensor operators, which are operators that act on multiple particles simultaneously.

2. What are 6j/9j symbols?

6j/9j symbols are mathematical coefficients used in the calculation of rotational coupling between two or more particles. They represent the quantum mechanical coupling of angular momenta between different particles and can be used to determine the probability of a specific interaction occurring.

3. How are tensor coupling and 6j/9j symbols related?

Tensor coupling is used to calculate the rotational coupling between particles, and 6j/9j symbols are used in this calculation to determine the probabilities of different coupling scenarios. They are both important tools in understanding the quantum mechanical interactions between particles.

4. What is the significance of the values of 6j/9j symbols?

The values of 6j/9j symbols are significant because they represent the probability of a specific quantum mechanical interaction occurring. These values can provide insight into the behavior of complex systems and can be used to make predictions about the outcomes of experiments.

5. How are 6j/9j symbols used in experimental physics?

6j/9j symbols are used in experimental physics to determine the probabilities of different coupling scenarios between particles. These values are then compared to experimental data to validate theoretical predictions and gain a better understanding of the behavior of quantum mechanical systems.

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