Undergrad Expectation value in terms of density matrix

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The discussion centers on the expectation value in quantum mechanics as described by Susskind's treatment of the density matrix. The equation presented, involving the trace of the product of an observable and the density matrix, is confirmed to be correct. The participants clarify the role of the trace operation in calculating expectation values. A participant initially expresses confusion about the trace but later resolves their uncertainty. This highlights the importance of understanding the mathematical framework in quantum mechanics.
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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.
 

Thread 'One does not “prove” the basic principles of Quantum Mechanics'

I am slowly going through the book 'What Is a Quantum Field Theory?' by Michel Talagrand. I came across the following quote: One does not" prove” the basic principles of Quantum Mechanics. The ultimate test for a model is the agreement of its predictions with experiments. Although it may seem trite, it does fit in with my modelling view of QM. The more I think about it, the more I believe it could be saying something quite profound. For example, precisely what is the justification of...
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