Expectation value in terms of density matrix

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SUMMARY

The discussion centers on the expectation value calculation using a density matrix as outlined in Susskind's textbook. The equation presented, ##\langle L \rangle = Tr \; \rho L = \sum_{a,a'}L_{a',a} \rho_{a,a'}##, accurately represents the expectation value of an observable ##L## with respect to a density matrix ##\rho##. The participant initially questioned the trace operation in the equation but later confirmed their understanding. This highlights the importance of clarity in quantum mechanics notation and operations.

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entropy1
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It says in Susskind's TM:

##\langle L \rangle = Tr \; \rho L = \sum_{a,a'}L_{a',a} \rho_{a,a'}##

with ##a## the index of a basisvector, ##L## an observable and ##\rho## a density matrix. Is this correct? What about the trace in the third part of this equation?
 
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Never mind, I see it now. Thanks.
 

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