How to Find the Final State and Probability After Measuring \(L_x^2\)?

AI Thread Summary
To find the final state after measuring \(L_x^2\) and obtaining a result of 0, the initial state in the \(L_z\) basis must be expressed in terms of the eigenstates of \(L_x\). The measurement collapses the state to the corresponding eigenstate of \(L_x\) associated with the eigenvalue of 0. The probability of obtaining this result can be calculated by projecting the initial state onto the eigenstate of \(L_x\) that corresponds to the measured value. The discussion highlights the need to clarify the relationship between the states in different bases and the process of measurement in quantum mechanics. Understanding these concepts is crucial for accurately determining the final state and its probability.
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Homework Statement



consider the state (\frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}}) in L_z basis. If L_x^2 is measured and the result of 0 is obtained, find the final state after the measurement. How probable is this result?

The Attempt at a Solution



I'm not sure if the state is superposition of the known ground states of L_x in L_z representation. How to find the state of the system after the measurement? And should I sum the probabilities of getting each of that state eigenvalues?

thanks.
 
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any moderator, please move my question to quantum physics forum. thanks.
 

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