Double slit experiment with spin

[abomination5]

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

 

[abomination5]

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,+>.

 

[Entropia]

Hello Abomination5,

Thank you for your question. The double slit experiment is a fundamental experiment in quantum mechanics that has been used to demonstrate the wave-particle duality of matter. In this experiment, a beam of particles, such as electrons, is passed through two parallel slits and the resulting pattern on a screen is observed.

In the case of particles with spin, such as electrons, the spin state of the particle can also be considered in the experiment. This means that the particle can have a certain orientation of its intrinsic angular momentum, which can be either "up" or "down" in the case of spin-1/2 particles like electrons. This adds an extra degree of freedom to the experiment.

When the electrons passing through slit A are of spin up and the electrons passing through B are of spin down, they are in different eigenstates, or states of definite spin. This means that they have different probabilities of passing through the slits and reaching the screen. As a result, the interference pattern that would normally be observed with particles of the same spin state is disrupted, and only the sum of the individual intensities is observed.

This can be explained by the principle of superposition in quantum mechanics, which states that the total state of a system is a combination of all possible individual states. In this case, the different spin states of the electrons passing through the slits interfere with each other, resulting in a different pattern on the screen.

I hope this helps clarify the concept for you. Please let me know if you have any further questions.