Chained Stern-Gerlach
- Quantum Mechanics Stern-Gerlach Quantum Measurement Spin-1/2
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Quantum Fundamentals 2021
Consider the Stern-Gerlach set-up shown, with a thermal oven” source, and some state vectors associated with various analyzer outputs:
How many particles were released from the oven? Calculate it exactly but also make a more conceptual/quick way to determine the (approximate, likely) answer. Describe both ways.
Write down Dirac notation expressions for \(|\Psi_a \rangle\), \(|\Psi_b \rangle\), \(|\Psi_c \rangle\) and \(|\Psi_d \rangle\) in the \(S_z\)-basis.
Student A says, “While going through the y-analyzer (Analyzer 2), the y-analyzer changes its incoming particles from being all z+ to an output which is a mixture of half of the particles being in the z+ state and half being in the z- state. That's why the farthest right z-analyzer (call it Analyzer 3) measures half z+ and half z-.”
Student B says, “No that's not right, all the particles entering Analyzer 3 are in the same state: they are in both the z+ and z- at the same time, they are all in a state that is a specific superposition of z+ and z- states, which is \(|\Psi_b\rangle\).”
Student C says, “There's no way to tell the difference between those two cases. So your argument doesn't matter in practice.”
Student D states, “Student B is right (sorry for the formality, B), and A and C are wrong, especially C.”
Describe a simple experiment (or experiments) and use a clear logical argument to show that Student D is correct (including the idea that C is wrong). Draw diagrams to make your case easier to comprehend. (Hint: Figure 1.12 in McIntyre might be helpful.)