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 Ŝ̟ corresponding to the eigenvalues ħ/2 and -h/2, respectively. (a) Verify that |V) is normalized. (b) Compute a = (V|Ŝ.|V) and b = (|(Ŝ.)*|¥), then find vb – a². (We will discuss these quantities later in class.) %3D
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 Ŝ̟ corresponding to the eigenvalues ħ/2 and -h/2, respectively. (a) Verify that |V) is normalized. (b) Compute a = (V|Ŝ.|V) and b = (|(Ŝ.)*|¥), then find vb – a². (We will discuss these quantities later in class.) %3D
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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 Ŝ̟ corresponding to the eigenvalues ħ/2 and
-h/2, respectively.
(a) Verify that |V) is normalized.
(b) Compute a = (V|Ŝ.|V) and b = (|(Ŝ.)*|¥), then find vb – a². (We will discuss
these quantities later in class.)
%3D
Expert Solution
Step 1
(a)
Given:
An electron is prepared in a quantum state which is described by .
Eigenvalues of are and .
Introduction:
The Stern Gerlach experiment was used to demonstrate that atoms have intrinsic angular momentum which is quantized. The setup was to send them through a magnetic field and observe the deflection. Silver atoms were used for this in the first experiment, and two distinct dots were seen from the deflected atoms.
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