Consider a device we will call a “spin-1/2 filter.” This simply consists of Ster

Question

Consider a device we will call a “spin-1/2 filter.” This simply consists of Stern-Gerlach apparatus where one of the two
outgoing beams of electrons is blocked, so that only the other beam emerges. Suppose we employ two such filters in
succession.
a. Discuss what emerges from the second filter compared to what goes in the first filter for each of the following cases.
i. The filters are arranged so that their north and south magnets are aligned in the same manner.
ii. The filters are arranged so that their north and south magnets are rotated through 180º with each other.
iii. The filters are arranged so that their north and south magnets are at right angles to each other.
b. Discuss how this compares with the filtering phenomenon we see with light passing through polaroids.

Explanation / Answer

1) When the filters are arranged in the similar manner, the two are spin-1/2 filters only and whatever electrons passed through first filter will also pass through second filter.

2) When the poles are rotated by 180 deg then one will act as spin-1/2 and another acts as spin--1/2 filetr. So the beams will be completely blocked.

3) When two are perpendicular then one will filetr the spin-1/2 electrons in z-direction and the second filetr acts as spin-1/2 filter in y-direction. So half of the electrons coming from the first filter pass through second filter.

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