How Are Spin 1 Particles Represented in Quantum Mechanics?

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SUMMARY

In quantum mechanics, a spin 1 particle measured to have m=1 along the x direction is represented by an eigenvector of the S_x operator with an eigenvalue of 1. The spinor state can be expressed as a column vector (1,0,0) in the x basis, which remains valid in the z basis due to the properties of SU(2) representations. To accurately determine the spinor state, one must apply the S_x matrix to a general state vector (a,b,c,d) and solve for the eigenvalues, ensuring normalization of the resulting vector.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically spin and measurement.
  • Familiarity with SU(2) representations and their significance in quantum mechanics.
  • Knowledge of eigenvalues and eigenvectors in linear algebra.
  • Proficiency in matrix operations, particularly with spin matrices like S_x.
NEXT STEPS
  • Study the properties and applications of SU(2) in quantum mechanics.
  • Learn about the derivation and implications of spin matrices, particularly S_x, S_y, and S_z.
  • Explore the normalization process for quantum states and its importance in quantum mechanics.
  • Investigate the role of measurement in quantum mechanics and how it affects spin states.
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Quantum mechanics students, physicists specializing in quantum theory, and anyone interested in the mathematical representation of spin systems.

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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