For Q1 Q3 consider the following experimental set up An ato

For Q1 – Q3 consider the following experimental set up: An atom in the state |?z > is shot into the following line of three Stern-Gerlach analyzers. Analyzer A is tilted at an angle of –? from the vertical, Analyzer B at +?, and Analyzer C at –?.

1) What is the probability the atom exits from the plus-channel of Analyzer C? Express your answer as a decimal: 0.XXX.

2) What is the probability the atom exits from the minus-channel of Analyzer C? Express your answer as a decimal: 0.XXX

(Hint: Careful! Don’t answer too quickly, based on your answer from the previous question. You need to analyze this separately.)

3) Given these probabilities don’t add to 1, where did the other incoming atoms entering the chain go?

Solution

explanation:

If the spin is initially up along a given axis, measuring along an axis at angle has outcomes up or down with probabilities cos²(/2) and sin ² (/2).

1. 0.170 (=cos2(20)*cos2(35)*sin2(50))

2. 0.120 (=cos2(20)*cos2(35)*cos2(50))

3. the sum of probabilities isnt 1 because the -(-alpha) and +(-alpha)+(+beta) spins atoms are discarded.