Zeeman Effect with a matrix involved

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Discussion Overview

The discussion centers around the Zeeman Effect, specifically focusing on the equation of motion for an electron in a magnetic field and its representation in matrix form. Participants are exploring the mathematical formulation and the assumptions involved in deriving the matrix from the equation of motion.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the equation of motion for an electron in a magnetic field and requests clarification on the arrangement of the corresponding matrix.
  • Another participant suggests that the matrix is derived by assuming each component of position is of the form exp(i*omega*x) and working through the equations to rewrite them in matrix form.
  • A request for further elaboration on the assumption is made, indicating a need for deeper understanding of the derivation process.
  • One participant challenges the need for further assistance, suggesting that the original poster should be able to derive the result independently.

Areas of Agreement / Disagreement

Participants express differing levels of understanding and willingness to assist, with some seeking clarification while others imply that the derivation should be straightforward. No consensus is reached on the clarity of the matrix arrangement or the necessity for further explanation.

Contextual Notes

Limitations in the discussion include a lack of detailed explanation regarding the assumptions made in the derivation and the specific steps taken to arrive at the matrix form. The resolution of the mathematical steps remains unresolved.

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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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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.
 
Yes, that's true, your assumption is written also.. Can you please elaborate more?
 
Do you have a more specific question? You should be able to work it out yourself to get the result.
 

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