What Do Expectation Values Tell Us About Quantum State Probabilities?

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SUMMARY

The discussion centers on the interpretation of expectation values in quantum mechanics, specifically regarding the x component of angular momentum (Lx). It is established that expectation values do not provide information about individual probabilities of quantum states. The assertion that probabilities can be complex numbers, such as i/3, is incorrect; probabilities must be real numbers within the range of 0 to 1. Therefore, the probability of measuring 0 h bar is not necessarily zero, but it cannot be derived from expectation values alone.

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  • Understanding of quantum mechanics principles
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jaobyccdee
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In measuring the x component of angular momentum of a state, by using the expectation value calculation of Lx, i got i/3 h bar - i/3 h bar, does this means that the probability of h bar is i/3 and the probability of 0 h bar is 0 and the probability of -h bar is i/3? If so, when is the probability of 0 h bar not 0?
 
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No, expectation values tell you nothing about the individual probabilities. Also, probabilities are real numbers between 0 and 1. It makes absolutely no sense to talk of a probability of i/3.
 

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