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,+>.