1. An electron prepared in a quantum state described by |V) = (v3/2)|+) + (i/2)|–) enters a series of Stern-Gerlach apparatuses below: SG SG2 Detector Here |+) and |-) are the eigenvectors of Ŝ, corresponding to the eigenvalues h/2 and -h/2, respectively. (a) Verify that |V) is normalized. (b) Compute a = (V\Ś.|V) and b = (V|(Ŝ.)°\W), then find o – a². (We will discuss these quantities later in class.) (c) Let the magnetic field of SG1 pointing in the y direction and the magnetic field of SG2 pointing in the z direction. Find the probability that the particle is detected.
1. An electron prepared in a quantum state described by |V) = (v3/2)|+) + (i/2)|–) enters a series of Stern-Gerlach apparatuses below: SG SG2 Detector Here |+) and |-) are the eigenvectors of Ŝ, corresponding to the eigenvalues h/2 and -h/2, respectively. (a) Verify that |V) is normalized. (b) Compute a = (V\Ś.|V) and b = (V|(Ŝ.)°\W), then find o – a². (We will discuss these quantities later in class.) (c) Let the magnetic field of SG1 pointing in the y direction and the magnetic field of SG2 pointing in the z direction. Find the probability that the particle is detected.
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Please do A, B, and C
Transcribed Image Text:1. An electron prepared in a quantum state described by |V) = (v3/2)|+) + (i/2)|–)
enters a series of Stern-Gerlach apparatuses below:
SG
SG2
Detector
Here |+) and |-) are the eigenvectors of Ŝ, corresponding to the eigenvalues h/2 and
-h/2, respectively.
(a) Verify that |V) is normalized.
(b) Compute a = (V\Ś.|V) and b = (V|(Ŝ.)°\W), then find o – a². (We will discuss
these quantities later in class.)
(c) Let the magnetic field of SG1 pointing in the y direction and the magnetic field of
SG2 pointing in the z direction. Find the probability that the particle is detected.
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