Question
Asked Dec 3, 2019
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It's a quantum mechanics question.

Consider an orbit al angular-momentum eigenstate l = 2, m = 0). Suppose that that state is rotated
about the y-axis by an angle B. Find the probability for the new state to be found in m = 0,±1,±2
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Consider an orbit al angular-momentum eigenstate l = 2, m = 0). Suppose that that state is rotated about the y-axis by an angle B. Find the probability for the new state to be found in m = 0,±1,±2

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Expert Answer

Step 1

Using the definition for matrix elements for rotation about y axis,

-i,B
j.m
DB)j.m exp
m.m
Here
J,J.m)= mh|j,m)
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-i,B j.m DB)j.m exp m.m Here J,J.m)= mh|j,m)

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Step 2

Probability for the new state to be found in m = 0, ±1, ±2 is,

-iJB
D(0,B.y=0=2,m exp
2, m
Here,
a,B.yare Euler angles
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-iJB D(0,B.y=0=2,m exp 2, m Here, a,B.yare Euler angles

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Step 3

By definiti...

47T
*(B.a)
211
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47T *(B.a) 211

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