Double slit experiment with spin

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SUMMARY

The discussion centers on the double slit experiment involving electrons with distinct spin states, specifically spin up and spin down. It is established that when electrons passing through slit A are in the |A,+> eigenstate and those through slit B are in the |B,-> eigenstate, no interference pattern occurs. This is due to the differing eigenstates preventing the formation of a coherent superposition necessary for interference, resulting in only the sum of individual intensities being observed.

PREREQUISITES
  • Understanding of quantum mechanics concepts, specifically eigenstates.
  • Familiarity with the double slit experiment and its implications in quantum physics.
  • Knowledge of spin states in quantum particles.
  • Basic grasp of linear combinations in quantum state representation.
NEXT STEPS
  • Study the implications of eigenstates in quantum mechanics.
  • Research the double slit experiment with varying particle properties.
  • Learn about quantum superposition and its role in interference patterns.
  • Explore the concept of spin in quantum mechanics and its measurement techniques.
USEFUL FOR

Students of quantum mechanics, physicists interested in particle behavior, and educators seeking to explain the double slit experiment with spin states.

abomination5
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Hi everyone,

I have a question concerning the double slit experiment that I would like clarified. According to a book I am reading if the electrons passing through slit A are of spin up and the electrons passing through B are of spin down then there will be no interference pattern (just the sum of the individual intensities).

According to the book this is because "the eigenstate of the electrons passing through slit A is different then the eigenstate of the system passing through B." I agree with this but I don't see how it leads to no intensity pattern.

Thanks for your help,
Abomination5
 
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Well, I think I figured it out but if you have any insightful comments please go ahead!

The reason is that the eigenstate of particles going through A is |A,+> and through B is |B,->. Now if both were known to be spin up then we couldn't know the eigenstate of a single electron traveling through A or B. It is just some linear combination a|A,+> + b|B,+>.
 

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