3. The component of angular momentum in the xz plane along an angle e to the z axis is classically Satisfy yourself that: Se S₁ = S₂cos + S₁ sin So = h COS A sin sin 0 -cos Show that the normalised eigenvectors are: (0) Xxx x+) = (cos(0/2)) sin(0/2) X(0) = (cos(012). () Show that these results are consistent with the Sx and Sz matrices. Hints: h - ½ (1) - 21 (6) = 2 Sz sin(A + B) sin A cos B + cos A sin B cos(A+B) = cos A cos B - sin A sin B
3. The component of angular momentum in the xz plane along an angle e to the z axis is classically Satisfy yourself that: Se S₁ = S₂cos + S₁ sin So = h COS A sin sin 0 -cos Show that the normalised eigenvectors are: (0) Xxx x+) = (cos(0/2)) sin(0/2) X(0) = (cos(012). () Show that these results are consistent with the Sx and Sz matrices. Hints: h - ½ (1) - 21 (6) = 2 Sz sin(A + B) sin A cos B + cos A sin B cos(A+B) = cos A cos B - sin A sin B
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Transcribed Image Text:3. The component of angular momentum in the xz plane along an angle e to the z axis
is classically
Satisfy yourself that: Se
S₁ = S₂cos + S₁ sin
So
=
h
COS A
sin
sin 0
-cos
Show that the normalised eigenvectors are:
(0)
Xxx
x+) = (cos(0/2))
sin(0/2)
X(0) = (cos(012).
()
Show that these results are consistent with the Sx and Sz matrices.
Hints:
h
- ½ (1) - 21 (6)
=
2
Sz
sin(A + B) sin A cos B + cos A sin B
cos(A+B) = cos A cos B - sin A sin B
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