Lecture 8: The Density Operator
•
The goal of quantum mechanics is to make
predictions regarding the outcomes of
measurements
•
Using the formalism we have developed so far,
the procedure is as follows:
–
Take an initial state vector
–
Evolve it according to Schrödinger's equation until
the time the measurement takes place
–
Use the projector onto eigenstates of the
observable to predict the probabilities for
different results
–
To confirm the prediction, one would prepare a
system in a known initial state, make the
measurement, then reprepare the same initial
state and make the same measurement after the
same evolution time. With enough repetitions, the
results should show statistical agreement with the
results of quantum theory
Expectation Value
•
The expectation value of an operator is defined
(with respect to state

!
"
) as:
•
The interpretation is the average of the results
of many measurements of the observable
A
on a
system prepared in state

!
"
.
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 Fall '08
 MichaelMoore
 mechanics, #, Quantum state, density operator

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