Angular momentum and group representation

• paweld
In summary, there are several recommended textbooks that discuss the relationship between angular momentum operators, eigenvectors, and the SO(3) or SU(2) group in quantum mechanics. These books, including "Group Theory and Quantum Mechanics" by M. Tinkham and "Symmetry Principles in Quantum Physics" by Fonda and Ghirardi, focus on the mathematical aspects and provide precise explanations on this topic. The older books by Rose and Edmonds are also highly regarded.
paweld
I heard that angular momentum operators and their eigenvectors are realted to SO(3) or SU(2)
group. Does anyone know a good textbook which explain the connection between how group theory and quantum mechanics (especially angualr momentum). I'm interested rather in books which emphasizes mathematical aspects and are quite precise in this matter.

I think the two old books by Rose and Edmonds are still the best for this.
I don't remember their exact titles but they have "angular momentum" in them.

Check out the book by Fonda and Ghirardi: "Symmetry Principles in Quantum Physics".

1. What is angular momentum and why is it important in physics?

Angular momentum is a physical quantity that measures the amount of rotational motion an object has. It is important in physics because it helps us understand and predict the behavior of rotating systems, such as planets orbiting around a star or electrons orbiting an atom.

2. How is angular momentum related to group representation?

In physics, group representation is a mathematical tool that helps us describe the symmetries and transformations of a physical system. Angular momentum is related to group representation because it can be represented as a vector in a mathematical space, and this vector can be transformed under rotational symmetries.

3. Can you explain the concept of orbital angular momentum and its mathematical representation?

Orbital angular momentum is the angular momentum of a particle due to its motion around a fixed point or axis. It is represented mathematically using the cross product of the position vector and momentum vector of the particle. This results in a vector quantity with magnitude and direction, which represents the amount and direction of the orbital angular momentum.

4. What is spin angular momentum and how is it different from orbital angular momentum?

Spin angular momentum is the intrinsic angular momentum of a particle, which arises from its quantum mechanical properties. It is not due to the particle's physical motion, unlike orbital angular momentum. Spin angular momentum is also quantized, meaning it can only take on certain discrete values, while orbital angular momentum can have any value.

5. How are angular momentum and group representation used in quantum mechanics?

In quantum mechanics, angular momentum and group representation are used to describe the symmetries and transformations of quantum systems, such as atoms and subatomic particles. They are also used to calculate the allowed energy levels and predict the behavior of these systems, providing a deeper understanding of the quantum world.

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