QM Measurement Problem: Expectation Value of Lz

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SUMMARY

The discussion centers on the quantum mechanics (QM) measurement problem, specifically regarding the expectation value of the angular momentum operator Lz when the system is in a state defined by Lx=1. The participant references Shankar's textbook on QM, highlighting the relationship between the eigenstates of Lx and the calculation of the expectation value of Lz. By identifying the eigenvector corresponding to Lx with eigenvalue 1, one can compute the expectation value of Lz for that state. The conversation emphasizes the importance of solving additional problems to deepen understanding of these concepts.

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  • Familiarity with quantum mechanics postulates
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  • Knowledge of eigenvalues and eigenvectors in linear algebra
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y.moghadamnia
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hi there,
I have been studying the postulates of QM in shankar book, and in the part it explains how measurement affects the system, it talks alittle about the expectation value and the uncertainty. then I came across this problem which I don't get. it gives three L(in x direcion), L(in y direction) and L(in z direction) matrices and then asks " take the state in which Lx=1. In this state what is the expectation value of Lz?" I don't understand this part:
how knowing Lx can help us calculate the expectation value of Lz?
 
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Given the matrix that represents Lx, you can write down the unique vector (up to a phase factor) that is an eigenvector of Lx with eigenvalue 1. Then you can calculate the expectation of Lz for this eigenvector.
 
aha, so that's the way u got to look at it. guess I should solve more problems to understand the way of looking at the problems.I asked people if they had good problems to send me but no one answered.
 

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