Problem 4. Consider the rigid rotor of problem 3 above. A measurement of Le is made which leaves the rotor in an eigenstate of Lx with value +ħ, i.e. (12) Find the probability that a measurement of L₂ yields the value -ħ. |) = |x; +1) = 2
Problem 4. Consider the rigid rotor of problem 3 above. A measurement of Le is made which leaves the rotor in an eigenstate of Lx with value +ħ, i.e. (12) Find the probability that a measurement of L₂ yields the value -ħ. |) = |x; +1) = 2
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![**PHY4355 Homework Set #8**
*Fall 2023*
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A rigid rotor with moment of inertia \( I \) is initially in the state:
\[
|\xi\rangle = \frac{1}{\sqrt{14}} \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}
\]
corresponding to the case \( \ell = 1 \).
(a) Write this state as a linear combination of the eigenstates of \( L_x \).
(b) Find the probability that a measurement of \( L_x \) yields the value \(-\hbar\).
---
**Problem 4.**
Consider the rigid rotor of problem 3 above. A measurement of \( L_x \) is made which leaves the rotor in an eigenstate of \( L_x \) with value \( +\hbar \), i.e.
\[
|\psi\rangle = |x; +1\rangle = \frac{1}{2} \begin{pmatrix} 1 \\ \sqrt{2} \\ 1 \end{pmatrix}
\]
Find the probability that a measurement of \( L_z \) yields the value \(-\hbar\).
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Transcribed Image Text:**PHY4355 Homework Set #8**
*Fall 2023*
---
A rigid rotor with moment of inertia \( I \) is initially in the state:
\[
|\xi\rangle = \frac{1}{\sqrt{14}} \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}
\]
corresponding to the case \( \ell = 1 \).
(a) Write this state as a linear combination of the eigenstates of \( L_x \).
(b) Find the probability that a measurement of \( L_x \) yields the value \(-\hbar\).
---
**Problem 4.**
Consider the rigid rotor of problem 3 above. A measurement of \( L_x \) is made which leaves the rotor in an eigenstate of \( L_x \) with value \( +\hbar \), i.e.
\[
|\psi\rangle = |x; +1\rangle = \frac{1}{2} \begin{pmatrix} 1 \\ \sqrt{2} \\ 1 \end{pmatrix}
\]
Find the probability that a measurement of \( L_z \) yields the value \(-\hbar\).
---
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