Wigner Matrix or Wigner D-Matrix?

In summary, the conversation discusses the Wigner Matrix and its relation to the Wigner D-Matrix. The person is confused about the difference between the two and is looking for clarification. They are informed that the Wigner Matrix is from the quantum transport equation and not the representation theory of SU(2). They also ask for a source to read more about it.
  • #1
TheDestroyer
402
1
Hello guys,

I'm reading the attached article, and I found there the Wigner Matrix, the first equation in the second page... is that the Wigner D-Matrix? I really got lost in that. It doesn't look like the Wigner D-Matrix I see everywhere, and it's not the so-called random matrix... anyone knows what that really is? please explain!

Thank you for any efforts.
 

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  • #2
It's not the Wigner D-matrix from the representation theory of SU(2), but the matrix of the Wigner function from quantum transport equation.
 
  • #3
Thank you for your reply.

Can that be found in some book? I don't know where to read about that.
 

1. What is a Wigner Matrix or Wigner D-Matrix?

A Wigner Matrix, also known as a Wigner D-Matrix, is a mathematical representation of the rotation and angular momentum of a physical system. It was developed by the physicist Eugene Wigner in the 1930s and is widely used in quantum mechanics and physics.

2. How is a Wigner Matrix used in quantum mechanics?

In quantum mechanics, a Wigner Matrix is used to describe the rotational symmetry of a physical system. This allows us to predict the probability of a particle's spin or angular momentum in a particular direction. It also helps to understand the behavior of particles in a magnetic field.

3. What is the difference between a Wigner Matrix and a Wigner D-Matrix?

The terms "Wigner Matrix" and "Wigner D-Matrix" are often used interchangeably. However, the Wigner D-Matrix is a specific type of Wigner Matrix that is used to represent the rotation of a physical system in three dimensions.

4. How is a Wigner Matrix related to the rotation group?

A Wigner Matrix is closely related to the rotation group, which is a mathematical group that describes the symmetry of a physical system under rotation. The elements of the rotation group are represented by the Wigner Matrix, which helps to understand the behavior of the system under different rotational transformations.

5. What are the applications of the Wigner Matrix?

The Wigner Matrix has many applications in physics, including quantum mechanics, nuclear physics, and solid-state physics. It is also used in engineering, particularly in the fields of signal processing and image analysis. Additionally, the Wigner Matrix has practical applications in areas such as crystallography, crystal optics, and astronomy.

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