Z-direction. Quantisation axis

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SUMMARY

The discussion centers on the concept of the quantisation axis in quantum mechanics, specifically addressing the use of the z-axis for measuring spin projections. The operators ##\hat{S}^+=\hat{S}_x+i\hat{S}_y## and ##\hat{S}^-=\hat{S}_x-i\hat{S}_y## are identified as the raising and lowering operators for spin projection. Participants emphasize that while the z-axis is commonly used, the choice of coordinate system is arbitrary and serves merely as a mathematical tool rather than a physical necessity.

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  • Understanding of quantum mechanics principles
  • Familiarity with spin operators in quantum physics
  • Knowledge of coordinate systems in mathematical contexts
  • Basic grasp of quantum state notation, such as ##|+\rangle## and ##|-\rangle##
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Students and professionals in quantum mechanics, physicists studying spin systems, and researchers interested in quantum computing methodologies.

LagrangeEuler
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I'm a bit confused with this concept of quantisation axis. ##|+\rangle## and ##|-\rangle## spin. And operators ##\hat{S}^+=\hat{S}_x+i\hat{S}_y## and ##\hat{S}^-=\hat{S}_x-i\hat{S}_y## are rising and lowering operator of spin projection. Why z-axis. How is measured that?
 
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Why z-axis.
The coordinate system is arbitrary, you could use any other axis as well. The coordinate system is just a mathematical tool, not something physical.
How is measured that?
What?
 

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