How Are Spin 1 Particles Represented in Quantum Mechanics?

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Discussion Overview

The discussion revolves around the representation of spin 1 particles in quantum mechanics, specifically focusing on the measurement of spin along different axes and the corresponding mathematical representations of spinor states. The scope includes theoretical aspects and conceptual clarifications regarding spin states and their eigenvectors.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether a spin 1 particle measured to have m=1 along the x direction would simply be represented by the column vector (1,0,0), or if it requires a more complex calculation involving the Sx matrix and normalization.
  • Another participant suggests using the three-dimensional representation of SU(2) to find the appropriate eigenvectors that correspond to the spinor states, indicating that an m=1 state along x is described by an eigenvector of S_x with eigenvalue 1.
  • A third participant expresses confusion regarding the term SU(2), indicating a need for clarification on this concept.
  • A later reply redirects the discussion to the appropriate forum for homework-related questions, suggesting that the original post may not belong in the current forum.

Areas of Agreement / Disagreement

Participants express differing levels of understanding regarding the representation of spin states and the use of SU(2). There is no consensus on the correct approach to determining the spinor state for a spin 1 particle.

Contextual Notes

There are unresolved assumptions regarding the definitions of spin states and the mathematical procedures involved in their representation. The discussion does not clarify the specific calculations or normalization processes required.

Simp
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Hi there,
I have a question, something that is confusing me.
If a particle of spin 1 is measured to have m=1 along the x direction, would the spinor state just be a column vector with (1,0,0), which would also be the spinor if x was infact z. OR would the spinor be determined by multiplying the Sx matrix by a column vector of (a,b,c,d) and letting this equal the eigenvalue (hbar in this case) muliplied by column vector (a,b,c,d) and working out their values and normalising.?
Thanks!
 
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Well, I would write down the three-dimensional representation of SU(2) and look for the appropriate eigenvectors (which you call spinor states). An m=1 state along x is described by an eigenvector of S_x with eigenvalue 1, right?
 
I am not sure what you mean by SU(2) ?
 
Simp, welcome to PhysicsForums.
However, your thread is in the wrong forum, as this is the Quantum Mechanics forum and not the Physics Homework forum. If you need assistance with your homework problems, may I direct you to the appropriate forum: https://www.physicsforums.com/forumdisplay.php?f=152
Thank you.
 

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