Zeeman Effect with a matrix involved

In summary, the conversation discusses the equation of motion for an electron in a magnetic field and its representation in matrix form. The equation is solved by assuming each component of the position vector is of the form exp(i*omega*x), and then rewriting the equations for each component in matrix form. The speaker also mentions that this assumption is written in their previous work and suggests working it out independently for a better understanding.
  • #1
M. next
382
0
Please refer to picture (1). This the equation of motion for an electron in a magnetic field along the z direction and moving with a certain velocity. Where Ω is the Larmor's frequency.
Then refer to picture (2), that is the matrix representing the previous equation. How was this matrix arranged. I didn't understand a thing.

Any help is much appreciated.
Please excuse me for the bad resolution of the images.
 

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  • #2
I think this is done by assuming that each component of r is of the form exp(i*omega*x). Then you put that in the first equation and work out what the equations are for each component and rewrite it in matrix form.
 
  • #3
Yes, that's true, your assumption is written also.. Can you please elaborate more?
 
  • #4
Do you have a more specific question? You should be able to work it out yourself to get the result.
 

1. What is the Zeeman Effect with a matrix involved?

The Zeeman Effect is a phenomenon where spectral lines in an atomic or molecular emission spectrum are split into multiple components due to the presence of a magnetic field. When a matrix is involved, it means that the atoms or molecules are embedded in a solid material rather than being free in a gas or plasma.

2. How does a matrix affect the Zeeman Effect?

The presence of a matrix can affect the Zeeman Effect in several ways. It can alter the strength and orientation of the magnetic field experienced by the atoms or molecules, which can change the splitting of the spectral lines. It can also introduce additional interactions between the atoms or molecules, leading to more complicated line splitting patterns.

3. What types of matrices are commonly used in Zeeman Effect experiments?

Matrices used in Zeeman Effect experiments include solids such as crystals, glasses, and polymers, as well as liquids and gels. These matrices are chosen based on their ability to host the atoms or molecules of interest and their compatibility with the experimental conditions.

4. How is the Zeeman Effect with a matrix involved studied?

The Zeeman Effect with a matrix involved is typically studied using spectroscopic techniques, such as absorption or emission spectroscopy. These techniques allow for the measurement of the splitting of spectral lines and the identification of different electronic and nuclear energy levels involved in the Zeeman Effect.

5. What are the applications of studying the Zeeman Effect with a matrix involved?

The Zeeman Effect with a matrix involved has various applications in materials science, chemistry, and physics. It can be used to study the electronic and magnetic properties of materials, as well as to investigate the dynamics of chemical reactions and physical processes in solid-state environments. It also has applications in developing new technologies, such as sensors and detectors.

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